given a committee of 8 women and 11 men, count the number of different ways of choosing a president, a secretary, and a treasurer, if the president must be a woman and the secretary and treasurer must be men. assume no one can hold more than one office.

Respuesta :

The president must be a woman and the secretary and treasurer must be men. assume no one can hold more than one office in one committee The correct answer is 1360.

Men's number is 11

There are 8 women.

Members total: 8 + 11 = 19

First, there will be 8 possible ways to choose 1 woman as president, and they are as follows: = 8C1 =8 Pete cannot serve as treasurer, thus one of the remaining 10 people will be chosen to serve in that capacity (11 - 1). There are 10 ways to choose 1 treasurer, and there are 10 ways total: = 10C1 = 10.

Thirdly, because no one is allowed to occupy more than one post, in this situation, one candidate will be chosen from a group of 10 males and 7 women.

As a result, there will be = 17C1 = 17 different ways to choose 1 person out of the available 17.

Thus, there will be 8 × 10 x 17 ways in all, which is 1360.

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