Question 1
Part a) 9 Athletes are running the 200M event. How many ways can the first three finishers be awarded medals? Show your work using the Permutation or Combination formula for full credit.




Part b) You have 10 photos to arrange in an art gallery, where there are 5 spaces to place them. How many ways can they be arranged? Show your work using the Permutation or Combination formula for full credit.





Part c) Write an original word problem of your own creation that uses a combination and the numbers 8 and 4. Also state the solution. You may not use a pizza-themed scenario.

Answers

Answer 1

Using the permutation and the combination formula, we have that:

a) The first three finishers can be awarded medals in 504 ways.

b) They can be arranged in 252 ways.

c) In how many ways can 4 students form a team from a set of 8.

If the order is important, the permutation formula is used.If the order is not important, the combination formula is used.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Permutation formula:

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Item a:

Order is important, as the finishers are ranked, hence:

[tex]P_{(9,3)} = \frac{9!}{6!} = 504[/tex]

The first three finishers can be awarded medals in 504 ways.

Item b:

The order is not important, hence:

[tex]C_{10,5} = \frac{10!}{5!5!} = 252[/tex]

They can be arranged in 252 ways.

Item c:

Situation in which the order is not important, hence, for example, in how many ways can 4 students form a team from a set of 8.

For more on permutation/combination, you can take a look at https://brainly.com/question/25247153


Related Questions

Jane wrote all natural numbers from 5 to 12. including 5 and 12.
how many numbers did Jane write?
PLS ANSWER FAST

Answers

Answer:

5, 6, 7, 8, 9, 10, 11 and 12 are the natural numbers between 5 and 12 including them, therefore Jane wrote 8 numbers. natural numbers start at positive 1 and go up by whole numbers infinitely, hope this helps

numbers in order from least to greatest?

35%, 3/5, 0.27, 2/7

Answers

Answer:

0.27, 2/7, 35%, 3/5

Step-by-step explanation:

Sarah is buying gifts for her friends. She is purchasing phone cases and chargers. The phone cases cost $25 and the charges cost $30. She

plans on spending no more than $100 and wants to buy at least 4 gifts. Which inequalities would be used to model this situation?

Answers

Answer:

Step-by-step explanation:

Let P be the number of phone cases and C the number of chargers.

p($25) + C($30) ≤ $100

and

P + C ≥ 4

After a power failure, the temperature in a freezer increased at an average rate of 3.5 °F per hour. The total
increase was 10.5 °F. Enter and solve an equation to find the number of hours until the power was
restored. Let x represent the number of hours it takes for the temperature to increase to 10.5 °F.

Answers

x=hours

7.5=2.5x

3=x

x=3

3 hours until the power was restored

Answer this question.

You get a thank you and 5 stars if it's the correct answer.

Answers

Answer:

w = 5, x = 7, y = 6, z = 12

Step-by-step explanation:

Evaluate each row by solving the corresponding equation, that is

row 1

4w = 20 ( divide both sides by 4 )

w = 5

row 2

2w + 2x = 24 ( substitute w = 5 )

2(5) + 2x = 24

10 + 2x = 24 ( subtract 10 from both sides )

2x = 14 ( divide both sides by 2 )

x = 7

row 3

w + 2x + y = 25 , that is

5 + 2(7) + y = 25

5 + 14 + y = 25

19 + y = 25 ( subtract 19 from both sides )

y = 6

row 4

w + x + y + z = 30 , that is

5 + 7 + 6 + z = 30

18 + z = 30 ( subtract 18 from both sides )

z = 12

A baseball team won about 62% of 162 games in a season.
About how many games did they win?

Answers

Answer:

the one about 100 games

Step-by-step explanation:

62 percent *162 =

(62:100)*162 =

(62*162):100 =

10044:100 = 100.44

this rounds to 100

Answer:

About 100 games

Step-by-step explanation:

162 * 0.62 = 100.4

100.4 rounded is 100

If -11 + N = -11, then N is the
a. additive identity
b. additive inverse
c. multiplicative inverse
d. multiplicative identity

Answers

Answer:

Step-by-step explanation:

eeuduehuheuhd  hbu h

please help finals study guide​

Answers

I
Dont seee any picture

Does (2, –2) make the equation y = –2x + –2 true?

Answers

Answer: no it doesn’t because -2 doesn’t equal to -6

Step-by-step explanation:

all you have to do is plug 2 for x value and -2 for y

-2= -2(2)+ -2

so -2= -4+ -2 and -4+ -2 is -6

therefor -2 doesn’t equal to -6

if 10 seeds are planted, what is the probability that exactly 3 don't grow?

Answers

Answer:

10:7

Step-by-step explanation:

take 10 as it is and it becomes 10

then,10-3 it is because when 3 don't grow it subtracts and becomes 7

Can someone please help?

Answers

Answer:

Well a midpoint makes the cutter segment or Line in exactly in half. So the two lines cutted are equal. In this case t is the midpoint. PT and TQ are equal. So you have two expressions, make then equal to each other since they are congruent.

6x+4=8x-8

12=2x

x=6

Now PT is 6x+4

So we subsitute x for 6 since x=6

6*6+4

40

PT is 40

Help a sis out ??
Write a function rule for the area of a triangle whose height is 4 in, more than twice the length
of its base. What is the area of the triangle when the length of its base is 16 in.?
A. A = 262 + b
C. A = 262 + b
A = 144 in?
A = 528 in.
B. A = b2 + 2b
A = 288 in
D. A = 262 + 4b
A = 576 in
O
D
B.
C
SES

Answers

Answer:

B

Step-by-step explanation:

let base be b then height h = 2b + 4

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height ) , then

A = [tex]\frac{1}{2}[/tex] b(2b + 4) ← distribute parenthesis

A = b² + 2b

When b = 16 , then

A = 16² + 2(16) = 256 + 32 = 288 in²

60 points!!! Please answer immediately and the entire page please I will also give you five stars

Answers

Answer:

Step-by-step explanation:

9.  Correct, D

-3Y + 9X <= 12

3Y - 9X => -12

3Y => -12 + 9X  

Y => -4 + 3X  

10.  D

11.  D

12.  Correct, B

13.  Correct, E

14.  A

15.  B

Someone helppp pls due in 5 min
I will thank

Answers

Angel 3 is adjacent to Angel 4 therefore they are equal.

Which graph best represents the solution to this system of inequalities?

A.
B.
C.
D.

Answers

Answer:

letter A po

Step-by-step explanation:

thanks for brain less

plz help its taxes!!! just questions not real lol

Answers

Answer:

pay: 32,000*12 ( since its per month) =384,000

income tax: 384,000*0.45 = 172,800

EI: 384,000*0.0173=6,643.20

CPP: 384,000*0.0495=19,008

Yearly Pay will be 384,000-172,800-6,643.20-19,008= $185,584.80

Weekly pay (paycheck) = 42320.91/52 = $ 3,568.25

Step-by-step explanation:

one more time what 4 + 4 × 4 + 4 ÷ 4=

Answers

Answer:

I think probably 21

Step-by-step explanation:

4+16+1 = 21

A swim team with 41 members decided to buy T-shirts that cost $15.75 each. 3. ___
What was the cost of the 41 T-shirts?

Answers

Answer:

The total cost would be $645.75

Explanation:

Multiply $15.75 by 3
41

Factorize 81xsquared+180x+100

Answers

Answer:

81x²+180x+1009x²+180x+10²using (a+b)²=a²+b²+2ab9x²+2(9x)(10)+10²(9x+2)²=(9x+2)(9x+2)

Pls help with question 3 and below

Answers

Step-by-step explanation:

now find the area of triangle and add with the area of square and subtract with the area of circle

hope it will help you

Consider a parallelogram with vertices at (0, 3), (2, 0), (4, 2), and (2, 5).
2) Suppose the parallelogram is reflected over the x-axis, which vertex of the parallelogram will have the same coordinate before and after the reflection?
A) (0, 3)
B) (2, 0)
C) (2, 5)
D) (4, 2)

Answers

Answer:

B

Step-by-step explanation:

So a reflection over the x is a change in the y value.

Only point (2,0) is on the x-axis, so it will not move.

Calculate the distance between the points M=(-1, -2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.

Answers

Answer:

nearest hundredth 8.944

Step-by-step explanation:

d = √((x2-x1)2 + (y2-y1)2)

Step by step procedure:

Find the difference between coordinates:

(x2-x1) = (-9 - -1) = -8

(y2-y1) = (2 - -2) = 4

Square the results and sum them up:

(-8)2 + (4)2 = 64 + 16 = 80

Now Find the square root and that's your result:

Exact solution: √80 = 4√5

Approximate solution: 8.944

Question 7 of 15 Which is an equation of the line through (0,0) and (5,-2)? O A. y = 3 B. y = ja c. y = - 30 D. y=- Y​

Answers

Answer:

b po sana po maka tulong

Step-by-step explanation:

pa brainliest po

PLS HELP ASAP ILL GIVE BRAINLKEST THANKS

Answers

Answer:

y = 5/6 x

Step-by-step explanation:

rise/run = slope

rise = 5

run = 6

so, 5/6 = slope

please answer i'll mark brainliest

Answers

Answer:

X=-10 Y=-3

Step-by-step explanation:

please help due any minute

Answers

Answer:

A the system has no solution

Step-by-step explanation:

Simplifying 2x + -5y = -8

Solving 2x + -5y = -8

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5y' to each side of the equation. 2x + -5y + 5y = -8 + 5y

Combine like terms: -5y + 5y = 0 2x + 0 = -8 + 5y 2x = -8 + 5y

Divide each side by '2'. x = -4 + 2.5y Simplifying x = -4 + 2.5y

Solution for 2x-5=12 equation:

2x - 5 = 12

2x = 12 + 5

2x = 17 (divide both sides by 2 to get x)

2x/2 = 17/2

x = 8.5

How do I solve this

Answers

D is the correct answer

Eva took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.10 plus $0.50 per mile. The total fare was $9.60, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.

Answers

Here we must write and solve a linear equation to find the number of miles that Eva traveled in the taxi. We will find that Eva traveled 11 miles.

So we know that the taxi charges a fee of $4.10 and then a plus of $0.50 per mile.

So if you travel for m miles, the cost equation is:

C(m) = $4.10 + $0.50*m

Now, we know that for Eva the total fare (total cost) was $9.60, then we need to solve:

$9.60 = C(m) = $4.10 + $0.50*m

$9.60 = $4.10 + $0.50*m

$9.60 - $4.10 = $0.50*m

$5.50 = $0.50*m

$5.50/$0.50 = m = 11

This means that Eva traveled 11 miles in the taxi.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/19045223

Answer:

11

Step-by-step explanation:

A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as long
the banner and the poster have perimeters 24 inches. What are the lengths and of widths of the poster and the banner?

Answers

Rectangular Poster:

Length = 9

Width = 3

Rectangular Banner:

Length = 10

Width = 2

Hope this is helpful!

A piece of timber is
x
cm long.
How long would 3 pieces of timber be put together in a line?

Answers

Answer:

3x cm long.

Step-by-step explanation:

If one piece is x cm

and there are 3 together, presumeabley the same length

then you'd just need to multiply the length 3 times, therefore 3x respresents multiplying x 3 times.

Have a good day!

Answer:

3x cm long

Step-by-step explanation:

3 times x is 3x

Other Questions
What Is the answer Plz it's urgent Tim is pushing a heavy box across the floor. He is using 300N of force and can accelerate at 2m/s/s. What is the mass of the box? -298 kg-600 kg-0.006 kg -150 kg Determine the amplitudeor period as requested.Period of y = 4sin 1/3xa. 4 b. Pi/4c. 4pi/3d. 6pi what is the output of the function when the input is 3 3 1/8 - b = 1 3/4how do I figure out what b is? Menciona dos palabras prestadas Historical Perspectives WhenChaucer wrote The Canterbury Tales,England was experiencing dramaticpolitical and social change as amiddle class began to emerge fromthe feudal system. How is thisdevelopment reflected in thePrologue? Work out the area of the triangle. The scale for anairplane is 1 cmfor 15 feet. If theplan is 9 cmlong, how long isthe actual plane? VOCABULARY Complete the sentences with the words from the box. help ASAP please hmmmm why is the high court and the supreme court of India known as the court of the records? Which system provides an easier way for people to communicate with a computer than a graphical user interface (GUI) SIMILARITIES between the first and second battle of panipat battlefield If f(x)=2x+1 and g(x)= x +3 find g(f(x)) and simplify completely. 15 more than the quotient of a number x and 12. DIRECTION: Below are statements describing the types of ingredients used in the preparation of sandwiches. ______________1. A staple food prepared by cooking a dough of flour and water and often additional ingredients. ______________2. Maybe beef, pork and sausage products. ______________3. Popular seafood which are highly perishable and should be kept chilled to moist as quality. ______________4. It moistens the bread and compliments the flavors of other ingredients. ______________5. These are relishes, olive oil and chutneys that give a lift to a sandwich. ______________6. Chicken or turkey breasts, tenderly cooked are seasoned. ______________7. These are indispensable in sandwich making because it add texture, flavor and color to sandwiches. ______________8. These are sliced thinly, firm texture, and act as binder, moistener of other ingredients. ______________9. It acts as a binder, moistener and other ingredients. ______________10. It refers to a food item made with two or more slices of bread with fillings between them. given f(x)=-3x^2-7x ,find f(7) the global patterns of atmospheric circulation and precipitation occur because of Does the light independent pathway of photosynthesis continue to occur when the leaf disks are placed in the dark environment