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There are five seniors in a class. For each situation, write how the binomial formula is used to calculate the probability.

AIn how many ways can I choose one senior to represent the group?
BIn how many ways can I choose two seniors to represent the group?
CIn how many ways can I choose three seniors to represent the group?
DIn how many ways can I choose four seniors to represent the group?
EIn how many ways can I choose five seniors to represent the group?

Verified Answer :

JcAlmighty
AThe answer is 5.

nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things

There are five seniors in a class: n = 5
I choose one senior: r = 1

nCr = n! / (r! (n - r)!)
5C1 = 5! / (1! (5 - 1)!)
       = (5 4 3 2 1) / (1 4!)
       = 120 / (4 3 2 1)
       = 120 / 24
       = 5

b) The answer is 10.

nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things

There are five seniors in a class: n = 5
I choose two seniors: r = 2

nCr = n! / (r! (n - r)!)
5C2 = 5! / (2! (5 - 2)!)
       = (5 4 3 2 1) / ((2 1) 3!)
       = 120 / (2 (3 2 1))
       = 120 / (2 6)
       = 120 / 12
       = 10


c) The answer is 10.

nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things

There are five seniors in a class: n = 5
I choose three seniors: r = 3

nCr = n! / (r! (n - r)!)
5C3 = 5! / (3! (5 - 3)!)
       = (5 4 3 2 1) / ((3 2 1) 2!)
       = 120 / (6 (2 1))
       = 120 / (6 2)
       = 120 / 12
       = 10


d) The answer is 5.

nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things

There are five seniors in a class: n = 5
I choose four seniors: r = 4

nCr = n! / (r! (n - r)!)
5C4 = 5! / (4! (5 - 4)!)
       = (5 4 3 2 1) / ((4 3 2 1) 1!)
       = 120 / (24 1)
       = 120 / 24
       = 5


e) The answer is 1.

nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things

There are five seniors in a class: n = 5
I choose five seniors: r = 5

nCr = n! / (r! (n - r)!)
5C5 = 5! / (5! (5 - 5)!)
       = (5 4 3 2 1) / ((5 4 3 2 1) 1!)
       = 120 / (120 * 1)
       = 120 / 120
       = 1

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