The mathletes club has 15 members and is electing a 5-member committee (president, vice-president, secretary, treasurer, and sergeant-at-arms). one of the members, alice, has set a condition that, if she is not elected president, then she will not accept any position in the committee. in how many ways can the club select the committee?

The total number of ways are 264,264

Step-by-step explanation:

Consider the provided information.

The Mathletes Club has 15 members and is electing a 5-member committee.

One of the members, Alice, has set a condition that, if she is not elected president, then she will not accept any position in the committee.

Case I: If she is elected as president.

If she is elected as president so now we have 14 members and is electing a 4-member committee. (vice-president, secretary, treasurer, and sergeant-at-arms).

No ways:

Case II: If she is not elected as president.

If she is not elected as president so now we have 14 members and is electing a 5-member committee. (president, vice-president, secretary, treasurer, and sergeant-at-arms)

No ways:

Hence, the total number of ways are:

24,024+240,240=264,264

Hence, the total number of ways are 264,264