Question

part 1 of 2
(a) the 2011 baseball team at ohio state university consisted of 12 freshmen, 12 sophomores, 8 juniors, and 9 seniors. the coaches want to choose two players from each class to represent the team at a booster club banquet. how many different ways can they make this choice?
the coaches can choose the players to represent the team at the booster club banquet in different ways.
part 2 of 2
(b) the coaches also need to choose two players overall to visit elementary schools in the community, with each player going to a different school. how many different ways can they make this choice?
the coaches can choose the players to visit the elementary schools in different ways.

Explanation:

Step1: Calculate combinations for part (a)

Use combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n=12 + 12+8 + 9=41\), \(r = 2\).
\(C(41,2)=\frac{41!}{2!(41-2)!}=\frac{41\times40}{2\times1}=820\)

Step2: Calculate permutations for part (b)

Use permutation formula \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 41\), \(r=2\).
\(P(41,2)=\frac{41!}{(41 - 2)!}=41\times40 = 1640\)

Answer:

(a) \(820\) different ways.
(b) \(1640\) different ways.