Question

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

a) In how many ways can I choose one senior to represent the group?
b) In how many ways can I choose two seniors to represent the group?
c) In how many ways can I choose three seniors to represent the group?
d) In how many ways can I choose four seniors to represent the group?
e) In how many ways can I choose five seniors to represent the group?

Answer 1

@jim_thompson5910

Answer 2

I got this but idk... :(a) n = 5 (5 seniors) and r = 1 (1 senior selected)
--> 5 ways

(b) (5 * 4) / 2 = 10 ways

(c) 10 ways

(d) 5 C(5-4) = 5C(1)
= 5 ways

(e) 1/1
= 1 way

Answer 3

In how many ways can I choose one senior to represent the group?

There are 5 ways because there are 5 seniors to choose from

Say you had seniors code named A, B, C, D, and E

There are only 5 ways to choose one letter

Answer 4

ok i got a as 5 too.

Answer 5

b?

Answer 6

10
10
5
1

my answers....

Answer 7

In how many ways can I choose two seniors to represent the group?

There are 5 ways to choose the first senior
There are 4 ways to choose the next

so there are 5*4 = 20 ways to choose 2 seniors but since order doesn't matter, you have to divide by 2 to eliminate double counting

so you're correct in saying (5*4)/2 = 10 ways

Answer 8

ok so b is 10

Answer 9

In how many ways can I choose three seniors to represent the group?

There are 5*4*3 = 60 ways to choose 3 seniors

But we overcount because order doesn't matter (ex: ABC is the same as CBA)

so because there are 3! = 6 ways to order ABC, this means we must divide by 6 to get 60/6 = 10

Answer 10

ok! so 10.. i got that too! now d?

Answer 11

There are 5*4*3*2 = 120 different ways to pick 4 people (out of 5)

Divide this by 4! = 24 to get 120/24 = 5

So that checks out as well

Answer 12

Finally, there is only one way to make a group of 5 people when you only have 5 people to choose from (assuming order doesn't matter)

So 5 C 5 = 1

In general, n C n = 1 for any positive integer n