A class consists of 20 sophomores and 15 freshmen the club n

A class consists of 20 sophomores and 15 freshmen. the club needs to choose four different members to president, vice president, secretary, and treasures. In how many ways is this possible? In how many ways is this possible if sophomores will be chosen as president and treasurer and fresh as vice president and secretary?

Solution

(a) Total number of students = 20 (sophomores) + 15 (freshmen) = 35

We need to select 4 people for the post of president, vice-president, secretary and treasurere

Number of ways = 35C4 = 52360 ways

(b) Total number of ways = 20C2(Selecting president and treasurer) * 15C2(selecting vice president and secretary)

=> 190 * 105

=> 19950 ways