You are planning a party. The space restriction is such that you can only invite 4 people. There are 9 friends to choose from. In how many ways can you select those 4 people?

a. There are (9-8+7+6(4+3+2+1) many ways.
b. There are (9-4)*(8-3)*(7-2)*(6-1) many ways.
c. There are 9*8*7*6 many ways.
d. There are 9*8*7*6/4*4*3*2*1) many ways.

Answers

Answer 1

Given:

Total number of friends = 9

Number of friend to invite = 4

To find:

The number of ways.

Solution:

We know that, total number of ways to select r items from n items is

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

So, the total number of ways to select 4 people from 9 friends is

[tex]^9C_4=\dfrac{9!}{4!(9-4)!}[/tex]

[tex]^9C_4=\dfrac{9!}{4!5!}[/tex]

[tex]^9C_4=\dfrac{9\times 8\times 7\times 6\times 5!}{4\times 3\times 2\times 1\times 5!}[/tex]

[tex]^9C_4=\dfrac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}[/tex]

Therefore, the required number of ways is [tex]\dfrac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}[/tex].

Note: All options are incorrect.


Related Questions

Pam drivers 14,735 miles in one year. The next year she drivers 13,869 miles. How many miles did she Drive in all?

Answers

Answer:28604 in total

Step-by-step explanation:

just copy and paste hope this helps

Answer:

28604 miles

Step-by-step explanation:

Just add the two numbers to get the total number of miles:

  14735

+ 13869=

  28604

Multiplying and Dividing Radicals

Simplify the following expressions.

Answers

the answer is 14. your welcome :)

25 POINTS! factor the trinomial:[tex]x^2-2x-2[/tex]

Answers

( x − 1 + i ) ( x − 1 − i )

Step-by-step explanation:

_____________ (x-1+i)(x-1-i)

What proportion results in the equation 9m=10n?

Answers

Answer:

the 2 nd one 9/m=10/n

Step-by-step explanation:

A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $720?

Answers

Answer:

At 5% , $300 was invested

At 15%, $4,700 was invested

Step-by-step explanation:

Let the amount invested at 5% be $x and the amount invested at 15% be $y

x + y = 5000 ••••••(i)

Let’s work with the interest;

5% of x + 15% of y = 720

0.05x + 0.15y = 720 •••••(ii)

From i;

x = 5000-y

Insert this into ii

0.05(5000-y) + 0.15y = 720

= 250 - 0.05y + 0.15y = 720

250 + 0.1y = 720

0.1y = 720-250

0.1y = 470

y = 470/0.1

y = $4700

x = 5000-y

x = 5000-4700 = $300

If 5 workers complete one task in 7 days, then how many days will 7 workers take to complete the same task?

Answers

Answer: 5 days

Step-by-step explanation:

5*7=35 - means the total amount of the days to complete the job by 1 worker is 35 days

So 7 workers can do this job in

35:7=5 days

Clayton opens a savings account with 11 dollars he got from his grandmother

Answers

Answer:

The answer is "$3640.58"

Step-by-step explanation:

This question is incomplete, that's why we add another question in the attached file. Please find it.

P = [tex]\$ \ 1300[/tex] and effective per year is = interest rate per year = 7.2  

Total  [tex]\$ \ 1300[/tex] due after 8 years is P+PRT:

[tex]\to 1300(1+0.072 \times 8)\\\\\to 1300(1+ 0.576)\\\\\to 1300(1.576)\\\\\to \$ \ 2048.8[/tex]

[tex]\to Total \ X = \$ \ (7000-2048.8) \\\\[/tex]

[tex]= \$ \ 4951.2 \\\\= X(1 +0.072 \times 5)\\\\=1.36 X \\\\[/tex]

The number of dollars is X [tex]= \frac{4951.2}{1.36} = \$ \ 3640.58[/tex]

The sum of three consecutive odd integers is 153. Find the three odd integers.

First integer =


Second integer =


Third integer =

PLEASE HELPPPP!!

Answers

Answer:

49, 51, 53

Step-by-step explanation:

Let the first odd integer be n.

Then the consecutive odd integer will be (n+2).

This will be followed by (n+4).

We know that the sum of these three is 153. In other words:

[tex]n+(n+2)+(n+4)=153[/tex]

Solve for n. Combine like terms:

[tex]3n+6=153[/tex]

Subtract 6 from both sides:

[tex]3n=147[/tex]

Divide both sides by 3:

[tex]n=49[/tex]

Therefore, our first odd number is 49.

So, our consecutive numbers must be 51 and 53.

Hence, our sequence is:

49, 51, 53

Notes:

If we get an even number for n or a non-integer value, then there are no three consecutive odd integers that sum to 153.

Answer:

49, 51, 53

Step-by-step explanation:

All odd numbers:

49 + 51 = 100

100 + 53 = 153

Last month, Jason’s dog drank about 728 ounces of water and his cat
drank about 252 ounces of water.
If Jason’s dog continues to drink this amount, how many ounces of water will he have consumed after 6 months? Show your work in the box below.

Answers

Answer:

131,040

Step-by-step explaination:

There is around 29-31 days in a month, so if you just round it's around 30 days a month.

30×6= 180 (days)

180×728= 131,040 ounces

jasons dog would drink 131,040 in 6 months.


Evaluate this expression.
112.212 - (- 3.25)

Answers

Answer:

115.462

Step-by-step explanation:

Answer: 115.462

Step-by-step explanation:

To start, the first thing we can observe is two negative signs, which we know turns into a positive sign.

Therefore, we now have:

112.212 + 3.25

115.462

Hope this helps!

The count of bacteria in a culture is 10 and doubles every 20 minutes. Find the population size after 11 hours. Can someone explain how to solve this?

Answers

Since you asked how to solve this, I will put the answer at the bottom.

You might not think the same way as I but I think in steps.

(1) Calculate how many times the bacteria divide in eleven hours

The bacteria divide every 20 minutes, and will therefore divide three times every hour, 60/20 = 3.

If the bacteria grow for eleven hours, each bacterium will divide 3 times per hour × 11 hours = 33 times.

(2) Add the orginial size of bacteria into the equation

(This part is edited)

(orginial size)*2^number of divisions

10*[tex]2^{33\\}[/tex]

=85899345920

a window washer clean 38 windows in 2 hours at this rate how many windows did he clean in 7 hours?​

Answers

Answer:

133 windows

Step-by-step explanation:

A rectangle is 3/5 red. The rest is blue and yellow, but not in equal ratios. What could those ratios be? PLEASE HELP

Answers

Blue can be 1/10 and yellow can be 3/10 or other way around.

Helpoooooooooooooooooooo

Answers

Answer:

1. x >/= -1

2. x < 4

3. x </= -1

4. x >/= -2

5. x < -3

6. x </= 7

Step-by-step explanation:

PEOPLE SHOW ANSWERS PLEASE AND WILL GIVE BRAINLIEST 8. The ratio of cats to dogs at a pet show
is 1:3.

a) What percent of the pets at the
show are cats?

Answers

Answer:

33.33%

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

so we add 1 and 3 together becuase since there are equal parts, we need to add to get the whole. so since the ration is 1:3, there are 1/4x cats thereate the show

I NEED HELP WITH THIS PICTURE IS PROVIDED

Answers

Is this an exam? Nehshdgdsusu



A Fahrenheit thermometer shows that the temperature is 13 degrees below zero. Enter the integer that represents the temperature in degrees Fahrenheit

Answers

Answer:

-13??? weird question... do you mean celcius themometer?

Step-by-step explanation:

Answer:

The integer that represents 13 degrees below 0 is -13°F.

Step-by-step explanation:

This is because the phrase "13 degrees below 0" is obviously not an integer meaning that the corresponding integer to this phrase would be -13.

P.S.

This question was asked by somebody else and I answered already so I am not copying the answer!

Hope this helps! :)

Please help it would help a lot

Answers

Answer:

1/2

Step-by-step explanation:

Answer:

y÷x 1÷2=1/2 This is the answer.

A birdbath is filled to the top. On Day 1, the volume of water in the bowl decreases by 7/8 cup. On Day 2, the volume in the bowl decreases by 3/4 cup. What number represents the total change in the volume of water in the bowl after two days? Write your answer as a mixed number.

Answers

Answer:

-1 5/8

Step-by-step explanation:

Let the total amount in the bowl be x;

If on Day 1, the volume of water in the bowl decreases by 7/8 cup, the remaining water will be;

x - 7/8

If on day 2, the volume in the bowl decreases by 3/4 cup, the remaining volume of water after the second day will be;

= x - 7/8 - 3/4

= x - (7-2(3))/8

= x - (7+6)/8

= x - 13/8

This shows that the total change after the two days is -13/8

As a mixed fraction;

-13/8 = -1 5/8

Factorise fully 2x+8

Answers

Answer:

2(x+4)

Step-by-step explanation:

To factor you have to divide both terms by the greatest common factor, which in this case is 2. Using distribution you can check your answer.

Answer: 2(x + 4)

Explanation: If you're asked to factor a polynomial,

the first thing you want to look for is the greatest common factor

for the terms that are involved.

The greatest common factor of 2x and 8 is 2.

So a 2 can factor out.

Inside the parenthses, we have each term divided by

the 2 that factored out of the polynomial.

So we have 2(x + 4).

y=_x+_ what would be the answer​

Answers

Answer:

y = -1/4x + 2

Step-by-step explanation:

slope = rise over run

-1 rise for 4 run

y intercept = 2

y = -1/4x + 2

X^2 + 10x = 0
How do I solve for a completed square ?

Answers

Answer:

12x=0

Step-by-step explanation:

x=0 because it is

Answer:

x = 0 x = -10

Step-by-step explanation:

First, use the AC method to figure out, what times what equals 0 and what adds up to equal 10, which would be 0 and 10.

Secondly, you would factor it out and be with

(x + 0)(x +10)=0

Third, you would set each one equal to 0

x + 10 = 0 x + 0 = 0

Solve from there to get your two x's

x = 0 and x = -10

1. An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.

Answers

Answer:

3 and 12

Step-by-step explanation:

3*5=15 and 15-3=12. The product of 3 and 12 is 36.

The integers are 3 and 12.

What is Algebra?

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

let the one integer be x.

Another integer = 5x - 3

According to question,

x *(5x-3 ) =36

5x ² -3 x =36

5x² -3 x - 36 = 0

5x² -15 x +12 x - 36 =0

5x( x-3) + 12 ( x -3) =0

(5x +12)( x- 3)=0

x= -12/5 or 3

So, the integers are 3 and 12.

Learn more about this concept here:

https://brainly.com/question/17023448

#SPJ2

find the value of x and the measure of MNW

Answers

Answer:

VALUE OF X:

3x-13+61 = 90

3x+48 = 90

3x = 42

x = 14

MEASURE OF <MNQ:

3x-13

= 3(14)-13

= 42-13

= 29

A company manufactures fuel tanks for cars. The total weekly cost (in dollars) of producing x fuel tanks is given by ... C(x) = 10000 +90x - 0.08x2 Find the exact cost of producing the 501st item.

Answers

Answer:

cost of producing the 501st item = $9.92

Step-by-step explanation:

The function representing the cost is given by;

C(x) = 10000 + 90x - 0.08x²

To get the cost of producing the 501st item, we have to first find the cost of producing 500 items and then do the same for 501 items then subtract the values gotten.

Thus;

C(500) = 10000 + 90(500) - 0.08(500)²

C(500) = 10000 + 45000 - 20000

C(500) = $35000

Similarly;

C(501) = 10000 + 90(501) - 0.08(501)²

C(501) = 10000 + 45090 - 20080.08

C(501) = $35009.92

cost of producing the 501st item = C(501) - C(500) = 35009.92 - 35000 = $9.92

7x – X – 1=4-7x + 21

Answers

Answer:

X=2

Step-by-step explanation:

FInd the circumference of a circle with a diameter of 6 yd. Use the value 3.14 for x and do not round your answers

Answers

Answer:

C ≈ 18.85yd

Step-by-step explanation:

write an equation of the line with a slope of -3/4 and y-intercept of -6

Answers

Answer:

y = -3/4x - 6

Step-by-step explanation:

Answer: y = (-3/4)x - 6

18% of the cars in the parking lot are blue.If there are 150 cars in the parking lot,how many cars are blue

Answers

Answer:

Step-by-step explanation:

14

write 6.085 in word form

Answers

six and eighty-five thousandths
Other Questions
Please can someone help me?? Ill give brainliest to the correct answer!! Which situation does NOT show causation?A) When the student population at a school increases, the number of teachers at the school increasesB) when the amount of sugar in a quart of apple juice is reduced, there are fewer calories in each serving C) When there are more workers on a project, the project is completed in less time.D) When there is more protein in an athletes diet, the athlete scores more points in a game. ______elements that have a longer half-life are more _______ than those that have a shorter half-life. Multiply the polynomial expressions below. (7x+5)(2x^3-4x^2+9x-3) A. 14x^4-18x^3+43x^2+24x-15 B. 14x^4-18x^3+43x^2+24x-8 C.9x^4-11x^3+16x^2+11-8 D.9x^4-11x^3+16x^2+11x-15 Leon is posting 12 flyers for the science club and 18 for the music club. He wants to make all the locations identical, with the same combination of science club flyers. In addition, he wants to make sure that no flyers are left over. What is the greatest number of locations that Leon can post at? You use a pair of shoes to measure a distance. The shoes are 10 3/4 inches long. The distance is equal to the length of 12 of the shoes. What is the distance? HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!!HELP ME! THIS IS REAL AND REALLY IMPORTANT!! HELP PLEASE!!Which of the following factors contributed most to the Bolivarian revolutionary movement? The passivity of the ruling class The reaction to increasing domestic tyranny The rise of a distinct Latin American ethnic identity The geographic distance between Spain and its colonies Which county leader enforces laws, makes arrests, and runs a jail? Find the prime factorization of 196. Use a method of your choice. List your final answer using exponents. Which statement best describes the significance of meiosis to sexual reproduction?A. It produces haploid gametes, with half the number of chromosomes.B. It creates organisms with better adaptability to the environment.C. It allows all types of cells to produce two sets of identical chromosomes.D. It produces up to eight diploid cells, each with the same number of chromosomes. .53^2 .6^3Standard form Solve.5 (2 3) < 5W + 20 Jonathan decides to go to an arcade Play some games. He sets a limit of $35 that he will spend PLEASE ANSWER BOTH!!!WILL GIVE BRAINLIEST!!!Taylor has a collision deductible of $500 and a Bodily Injury Liability coverage limit of $50,000. Taylor hits another driver and injures them severely. The case goes to trial and there is a verdict to compensate the injured person for $40,000.a) How much does Taylor have to pay?b) How much does Taylor's insurance pay? A backpack originally costs $35.It is on sale for $22.75. Find the percent of decrease.21 points bruh and also sub to RahimZ 12*PLEASE ANSWER FAST!!!!!!!! im failing in art....yea ART anyways can sumone give tips on how to draw better? Read the excerpt from White Fang. "Kiche!" the man cried again, this time with sharpness and authority. And then the cub saw his mother, the she-wolf, the fearless one, crouching down till her belly touched the ground, whimpering, wagging her tail, making peace signs. The cub could not understand. He was appalled. The awe of man rushed over him again. His instinct had been true. His mother verified it. She, too, rendered submission to the man-animals. Which best states the perspective of White Fang in the excerpt? A: She is preparing to attack the man to show her authority Aisha divides 15 meter of ribbon into 2 equal pieces.What is the length of each piece of ribbon? y = (x + 1)(x - 2)Distribution