Question

A country has two political parties, the Reds and the Blues. The 100-member senate has 4444 Reds and 5656 Blues. Each party must elect a chair and a vice chair from their party's members, and one person cannot be elected for both. How many different outcomes are there for the chair and vice chair elections of both parties

Answer 1

There are 5,827,360 different outcomes.

Explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In each party:

The order in which the people are selected is important(first is chair, second vice chair), which means that the permutations formula is used to solve this question.

Permutations formula:

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

`P_((n,x)) = (n!)/((n-x)!)`

Reds:

Two from a set of 44. So

`P_((44,2)) = (44!)/((44-2)!) = 44*43 = 1892`

Blues:

Two from a set of 56. So

`P_((56,2)) = (56!)/((56-2)!) = 56*55 = 3080`

How many different outcomes are there for the chair and vice chair elections of both parties?

Considering both, by the fundamental counting principle:

1892*3080 = 5827360

There are 5,827,360 different outcomes.