Twenty-eight students, of whom seven are seniors, are selected as semifinalists for a literary award. Of the twenty-eight students, fourteen finalists will be selected. In how many ways can the fourteen finalists contain five seniors?
A)6,172,530
B)817,190
C)40,116,600
D)21
E)293,930

Question

Quizplus · Accepted Answer

The number of ways to select 5 seniors out of 7 is 7C5 = 21. The number of ways to select 9 non-seniors out of 21 is 21C9 = 10,010. The number of ways to arrange the 14 finalists is 14! = 87,178,291,200. Therefore, the number of ways to select 14 finalists containing 5 seniors is 21 * 10,010 * 87,178,291,200 = 6,172,530.

Twenty-Eight Students, of Whom Seven Are Seniors, Are Selected as Semifinalists