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 you choose one senior to represent the group?

b) In how many ways can you choose two seniors to represent the group?

c.) In how many ways can you choose three seniors to represents the group?

d) In how many ways can you choose four seniors to represents the group?

e).) In how many ways can you choose five seniors to represents the group?

Answer 1

First, the question "in how many ways can I choose some members of a set to represent that set?" means "how many different choices (subsets) of that set are there?"

a) There are 5 seniors. Let's call them A, B, C, D, and E. You can choose the following one-member representations (one-element subsets): {A}, {B}, {C}, {D}, and {E}. How many choices are there? 5, as many as members.

The formula to calculate the number of different k-element subsets of an n-element set is written nCk ("n choose k") and defined as n!/(k!(n-k)!), where n! ("n factorial") is the product of all integers from 1 up to and including n: n!=1*2*...*n; additionally 0!=1.

In general, for any n, nC1 = n.

b) 5C2 = 5!/(2!(5-2)!) = 5!/(2!*3!) = (1*2*3*4*5) / ((1*2)*(1*2*3)) = (4*5)/(1*2) = 2*5 = 10.

In general, for any n, nC(n-1) = (1*2*...*(n-1)*n) / (1*2*...*(n-1)*1!) = n / 1! = n/1 = n.

c) 5C3 = 5!/(3!(5-3)!) = 5!/(3!*2!) = 5!/(2!*3!) = 10.

In general, for any n and any k between 0 and n inclusive, nCk = nC(n-k).

d) 5C4 = 5C(5-4) = 5C1 = 5.

e) 5C5 = 5!/(5!(5-5)!) = 5!/(5!*0!) = 1/0! = 1/1 = 1. There's only one way to choose five out of five: choose everybody. (In ancient Greek city-states, there was direct democracy: there were no representatives chosen to vote on your behalf; all eligible voters voted. Not every resident was an eligible voter, though.)

Answer 2

Thank you

Answer 3

Anytime.

Answer 4

can you help with one more I am going to post it

Answer 5

i will try.