(a) To choose four members out of 25 to serve on an executive committee, we can use the combination formula. The number of ways to choose four members is given by:
C(25, 4) = 25! / (4! * (25-4)!) = 25! / (4! * 21!) = (25 * 24 * 23 * 22) / (4 * 3 * 2 * 1) = 12,650 ways.
Therefore, there are 12,650 ways to choose four members of the club to serve on an executive committee.
(b) To choose a president, vice-president, secretary, and treasurer of the club where no person can hold more than one office, we can use the permutation formula. The number of ways to arrange four people in different positions is given by:
P(25, 4) = 25! / (25-4)! = 25! / 21! = 25 * 24 * 23 * 22 = 30,240 ways.
Therefore, there are 30,240 ways to choose a president, vice-president, secretary, and treasurer of the club.
A club has 25 members.(a) How many ways are there to choose four members of the club to
serve on an executive committee? (b) How many ways are there to choose a president, vice-
president, secretary, and treasurer of the club, where no person can hold more than one
office?
1 answer
1 answer