Suppose we want to choose to letters without replacement three letters a b and c. How many ways can this be done if the order of the choices is relevant? How many ways can this be done if the order of the choices is not relevant?

Answers

Answer 1

Answer:

6 ;

3

Step-by-step explanation:

Letters = (a, b, c)

Number of letters to be chosen = 2

If the order is relevant, then we use permutation :

nPr = n! ÷ (n-r)!

3P2 = 3! ÷ (3-2)!

3P2 = (3 * 2 * 1) ÷ 1

3P2 = 6

If the order is not relevant ; We use combination :

nCr = n! ÷ (n-r)!r!

3C2 = 3! ÷ (3-2)!2!

3C2 = 3! ÷ 1!2!

3C2 = (3 * 2!) ÷ 2! * 1

3C2 = 3


Related Questions

HELP ME PLS

If two points known on the line AB in the coordinate plane is (7,15) and (18,42), calculate the following..

A) the slope of the line AB

B) The length of the line AB

Answers

Answer:

Slope = 27/11

AB = 29.15 u

Step-by-step explanation:

Given :-

Two points are given to us .The points are A(7,15) and B(18,42)

To Find :-

The slope of the line .The length of line AB .

We can find the slope of the line passing through the points [tex]( x_1,y_1)[/tex] and [tex]( x_2,y_2)[/tex]as ,

[tex]\implies m = \dfrac{ y_2-y_1}{x_2-x_{1}}[/tex]

Plug in the respective values ,

[tex]\implies m = \dfrac{ 42-15}{18-7} \\\\\implies \boxed{ m = \dfrac{ 27}{11 }}[/tex]

Hence the slope of the line is 27/11 .

[tex]\rule{200}2[/tex]

Finding the length of AB :-

We can find the distance between them by using the Distance Formula .

[tex]\implies Distance =\sqrt{ (x_2-x_1)^2+(y_2-y_1)^2} \\\\\implies Distance =\sqrt{ (18-7)^2+(42-15)^2 } \\\\\implies Distance =\sqrt{ 11^2 + 27^2 } \\\\\implies Distance =\sqrt{ 121 + 729 } \\\\\implies Distance = \sqrt{ 850} \\\\\implies \boxed{ Distance = 29.15 \ units }[/tex]

Hence the length of AB is 29.15 units .

what is the LCM of the numbers 9, 21 using prime factorizations

Answers

What is the Least Common Multiple of 9 and 21? Least common multiple (LCM) of 9 and 21 is 63.
Give them Brainliest!

2) Bobby's chess team is made up of 10 boys and 8 girls.

What is the ratio of boys to girls on the chess team? (2 pt)

Answers

I believe it would be 10 : 8

Type the correct answer in each box. Tyler visited five friends at their respective houses. He started from his house at A and walked to his friend’s houses at B, C, D, E, and F in that order, before returning home to A. If each unit on the coordinate plane represents 1 block, the total distance that Tyler traveled is blocks. The area of the route he covered is square blocks.

Answers

the answer is 5

explenation

Tyler visited five friends at their respective houses. He started from his house at A and walked to his friend’s houses at B, C, D, E, and F in that order, before returning home to A.

If each unit on the coordinate plane represents 1 block, the total distance that Tyler traveled is  

16

blocks. The area of the route he covered is  

16

square blocks.

simple explenation: i took the test

Tyler visited five friends at their respective houses. The area of the route he covered is 16 square blocks.

How are scale drawings formed?

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

Tyler visited five friends at their respective houses.

He started from his house at A and walked to his friend’s houses at B, C, D, E, and F in that order, before returning home to A.

If each unit on the coordinate plane represents 1 block,

Then, the total distance that Tyler traveled is blocks.

Then, The area of the route he covered is 16 square blocks.

Learn more about scale factors here :

https://brainly.com/question/22312172

#SPJ2

The distance from Alison's house to the mailbox is 2/5 mile. The distance from the mailbox to the bus stop is 1/3 mile. What is the total distance from Alison's house to the bus stop? 3/15 11/15 5/6 3/8

Answers

Answer:

Option B is correct

Step-by-step explanation:

Given

Distance from Alison's house to the mailbox  = [tex]\frac{2}{5}[/tex] miles

Distance from the mailbox to the bus stop [tex]\frac{1}{3}[/tex] miles

The total distance between Alison's house to the bus stop is

[tex]\frac{2}{5} + \frac{1}{3} \\\frac{6+5}{15} \\\frac{11}{15}[/tex]

Hence, option B is correct

Which of the following numerical data sets has a mean of 40?
A) 18,82
B) 21, 34, 65
C) 38, 39, 40, 41
D) 20, 30, 40, 55

help!​

Answers

Answer:

The answer is B) 21, 34, 65

Step-by-step explanation:

21 + 34 + 65 = 120

120 divided by 3 = 40.

In order to find the mean you must add up all of the numbers in the numerical data set, then divide that by how many numbers there are. Hope this helps! :)

HELPPP PLZZZZ ASAP IS PLEASEEE DONT SEND A FILE AT ALL

Answers

Answer:

I am telling I am new to this

Whats the slope of the line?

Answers

Answer:

m = rise/run = 4/5.

Step-by-step explanation:

This line goes throught the "exact" grid intersections (-2, 0) and (3, 4).  As we move from the first point to the second, we see that x increases by 5 (this is the 'run') and y increases by 4 (this is the 'rise').  Thus, the slope of this line is m = rise/run = 4/5.

Make a chart of real number system

Answers

Answer:

we can only answer your question

Step-by-step explanation:

What is the slope of a line that has points (5,-3) and (11,5) ? Remember to simplify.

Answers

Answer:

slope= y²-y¹

x²-x¹

= 5--3

11-5

= 5+3

6

= 8

6

= 4/3

or 1.33

Tracy a teacher is and she's paid a monthly salary of $3,728 calculate her salary per annum

Answers

Answer:

$44,736

-

Hourly: $21.51

Daily: $172.06

Weekly: $860

Bi-Weekly: $1,721

Semi-Monthly: $1,864

Monthly: $3,728

Quarterly: $11,184

Annual: $44,736

Which factored polynomial is shown in the graph?
A) y = (x + 2)(x + 1)(x + 4)
B) y = (x + 2)(x − 1)(x + 4)
C) y = (x + 2)(x − 1)(x − 4)
D) y = (x − 2)(x − 1)(x + 4)

Answers

Answer:

B

Step-by-step explanation:

First, we can determine the zeros of the function.

We can see that the graph passes through the x-axis at the points: x = -4, -2, and 1.

Therefore, we have three factors:

[tex](x-(-4)),\, (x-(-2))\text{ and } (x-(1))[/tex]

Thus, our function will be:

[tex]y=(x+4)(x+2)(x-1)[/tex]

Our answer is B.

In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who has a sister also has a brother?


Answer 3/8​

Answers

Answer:

[tex]P(sister) = \frac{8}{30} \\ [/tex]

Step-by-step explanation:

[tex]P(sister) = \frac{8}{30} \\ P(brother) = \frac{13}{30} \\ P(SnB) = \frac{3}{30} \\ [/tex]

What percent is 12 of 32 need help quick

Answers

37.5% I believe12 ÷ 32 = 0.3750.375 = 37.5%Please let me know if I am wrong.

Answer:

37.5%

Step-by-step explanation:

got this question correct

Mathh please help and actually do it

Answers

Answer:

Parallel

Step-by-step explanation:

they have the same slopes

Answer:

i believe its b sir. brainliest?

Step-by-step explanation:

Please help
No link!

Answers

Answer:

Axis Of Symmtery x=-3 and the vertex is (-3,8)

Step-by-step explanation:

Jaime bakes24 muffins and gives away 3. She also bakes 36 bagels and gives away 4. Writean expression using GROUPING SYMBOLS ILLL GIVE BRAINLY!

Answers

Answer:

24-3=21 , 36-4=32 ,  3+4=7 , 7 x 5 , which equals 35

Step-by-step explanation:

can someone solve this
7x+4y=12
x+2y=-4

Answers

Answer:9.

Step-by-step explanation:7x -4y =9. 13x = 39. x = 3. 3(3) + 2y = 15. 9 +2y =15. 2y = 6y = 3. check: 7(3)

- 4(3) = 21 - 12 = 9.

Osetion Progress
Homework Progress
a cm
R
Dia
dra
In the diagram shown,
PQRS is a rectangle,
XY is parallel to PS,
RY = 9 cm,
Area of PQRS = 84 cm,
Area of PXYS = 21 cm.
Work out the values of a and b.
You must show all your working.
9 cm
ү
bcm
P
S

Answers

Answer:

The answer is below

Step-by-step explanation:

PQRS is a rectangle. The length of rectangle PQRS = 9 cm + b cm = (9 + b)cm

The breadth of PQRS = a. Hence:

Area of PQRS = length * breadth = (9 + b)(a) = 9a + ab

but Area of PQRS = 84 cm²

9a + ab = 84          (1)

In rectangle PXYS, length = QR = a cm, breadth = YS = b cm

Hence area of PXYS = length * breadth = (a)(b) = ab

But Area of PXYS = 21 cm²

ab = 21         (2)

substitute ab = 21 in equation 1:

9a + 21 = 84

9a = 84 - 21

9a = 63

a = 7 cm

ab = 21

7b = 21

b = 3 cm

Therefore a = 7cm, b = 3 cm

 

D'jair's vacation starts on July 18th and lasts one week. Kyoko's vacation is from July 18th to July 25th. Whose vacation was longer?

Answers

One week= 7 days
25-18=7
I believe both vacations are the same amount of time

ill give brainliest help

Answers

Answer:

9 cm

Step-by-step explanation:

Length = 72 / (4 x 2)

Length = 72 / 8

Length = 9 cm

Hope that helps! :)

-Aphrodite

Answer:

9 cm

Step-by-step explanation:

4 * 2 = 8

72/8=9

Which organism can no longer be found living on Earth?


horse


trilobite


fern


sponge

Answers

Answer:

trilobite

Step-by-step explanation:

trilobites are a group of extinct marine arthropods

HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP

Answers

Answer:

b 4 Lee's than 3 times Mary's age is 3x-4

Answer:

3x -4

Step-by-step explanation:

we know this because Charlenes age is - 4 than Marys age.

Now, how much is that something? 3x

3x -4

Suppose each license plate in a certain state has one digit, followed by four letters, followed by one digit. The letters F, O, S, and X and the digit 0 are not
used. So, there are 22 letters and 9 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using
this format?

Answers

Each digit can be 1 of 9 numbers.

Each letter can be 1 of 22 letters.

To find total combinations, Multiply each number of choices by each number of choices.

9 x 22 x 22 x 22 x 22 x 9 = 18,974,736 total combinations

The graph represents the distance in miles, y: that Car A travels in x minutes. The function y x represents the distance, y; that Car B travels in x minutes. Both cars are moving at a constant rate of speed. Which BEST compares the rates of the two cars? The rate of Car B is 1 of a mile per minute less than the rate of Car A 6 Bi The rate of Car A is of a mile per minute less than the rate of Car B. The rate of car B is 2 of a mile per minute greater than the rate of Car A. Car A and Car Bare traveling at the same rate per minute.​

Answers

Explain

More information
X
Step by step solutions

The path of a flying fish as it made its approach to the surface of the ocean and flew out of the water is represented by the quadratic function h(t) = -t2 + 6t - 5, where t represents the time, in seconds, and h(t) represents the fish's height and depth, in feet. Graph the function using the graphing calculator. To the nearest second, how long was the fish out of the water?

1 second
3 seconds
4 seconds
5 seconds

Answers

Answer:

4 seconds

Step-by-step explanation:

fish broke the water's surface in 1 second and went back into the water at 5 seconds

∴ it was out of the water for 4 seconds

Answer:

4

Step-by-step explanation:

Virginia had an average rainfall of 24 inches last year. This year it rained 10% more than last year. How many inches of rain fell this year?

Answers

Answer:

It rained 26.4 inches this year.

Step-by-step explanation:

10% of 24 is 2.4

24 + 2.4 = 26.4

Answer:

26.4

Step-by-step explanation:

100%=240

10%=2.4

110%=26.4

What’s the value of x

Answers

Answer:

x = 2

Step-by-step explanation:

According to the inscribed Angle Theorem, the size of an inscribed angle = ½(measure of the intercepted arc)

m<L = (7x + 9)° is an inscribed angle

m(KM) = 46° is its intercepted arc

Therefore:

7x + 9 = ½(46)

Multiply both sides by 2

2(7x + 9) = 46

14x + 18 = 46

14x + 18 - 18 = 46 - 18

14x = 28

14x/14 = 28/14

x = 2

So you wanna go shopping and you have 45$ to spend. you see a t shirt you like
for 15$, a pair of new shoes for 20$ and a holiday sweater for 10$, and some pants for 13$. Which two things should you buy to save the most money on your purchase?

Answers

Answer:

The holiday sweater and the pants will save the most money with having $22 left.

Step-by-step explanation:

have a good day :)

In Frank's piggy bank, there are only quarters
and dimes. He has 37 coins, and has a total of
$5.50. How many quarters does he have?

Answers

Answer:

12 quarters

Step-by-step explanation:

number of quarters ---------x

number of dimes ------------y

therefore, x + y = 37---------------times 10 both sides --------10x + 10y = 370-------equation 1

              0.25x + 0.1y = 5.5 -----times 100 both sides -------25x + 10y = 550 ------equation 2

equation 2 minus equation 1 is 25x + 10y - 10x - 10y = 550 - 370 ------ 15x = 180 -------x = 12

there are 12 quarters

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