Question

From a pool of six juniors and twelve seniors, four co-captains will be chosen for the football team. How many different combinations are possible if two juniors and two seniors are chosen?

Please help and show work

Answer 1

990 different combinations

Explanation:

There are 6 juniors and 12 seniors for a total of 16 students

Out of 6 juniors we have to pick 2 juniors

Out of 12 seniors we have to pick 2 seniors

The number of items r that we can pick from a larger set of n items is given by C(n, r) pronounced n choose r.. This is sometimes written as nCr

The formula forC(n, r) is

`\boxed{C(n,r) = (n!)/(r! (n - r)! )}`

where n! = n factorial = n x (n-1) x (n-2) x .... x 3 x 2 x 1

We can choose 2 juniors out of 6 juniors in C(6, 2) ways
and
2 seniors out of 12 seniors in C(12, 2) ways

`C(6, 2) = = (6!)/( 2! (6 - 2)! )\\\\= (6!)/(2! * 4! )\\\\= 15`

`C(12, 2) = (12!)/( 2! (12 - 2)! )\\\\ = (12!)/(2! * 10! )\\\\= 66`

Therefore the total number of ways you can select 2 juniors and 2 seniors from a pool of 6 juniors and 12 juniors

= 15 x 66 = 990

Answer 2

1 and 3

Explanation:

pick one from the junior side and 3 from seniors because the senior is more that the junoir