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

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: