SOLUTION: The table below shows the grade-level distribution for the school basketball team. freshman-2 sophomore-4 junior-8 senior-15 A local television station wants to interview 8

Question 1021686: The table below shows the grade-level distribution for the school basketball team.
freshman-2
sophomore-4
junior-8
senior-15
A local television station wants to interview 8 students from the team. How many different ways can exactly 4 seniors and 4 juniors be selected for the interview?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
The table below shows the grade-level distribution for the school basketball team.
freshman-2
sophomore-4
junior-8
senior-15
A local television station wants to interview 8 students from the team. How many different ways can exactly 4 seniors and 4 juniors be selected for the interview?

Solution:
Here the question is how many different ways can 4 seniors and 4 juniors be selected. So the freshmen and sophomores don't really count.
Seniors can be chosen 4 out of 15, so C(15,4) ways. Juniors can be chosen 4 out of 8, so C(8,4) ways.
The total number of ways is the product of the two, namely
= C(15,4)*C(8,4)
= 15!/(4!11!)*8!/(4!4!)
= 1365*70
= 95550 ways
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