Question

A certain committee consists of 18 people. from the committee, a president, a vice-president, ays can these 4 offica secretary, and a treasurer are to be chosen. in how many wes be filled? assume that a committee member can hold at most one of these offices.

Answer 1

There are 73,440 ways to fill the positions of president, vice-president, secretary, and treasurer from a committee of 18 people.

Step-by-step explanation:

To fill the positions of president, vice-president, secretary, and treasurer, we need to determine the number of ways these 4 offices can be filled from a committee of 18 people. Since a committee member can hold at most one office, we use the concept of permutations.

The number of ways to choose a president from 18 people is 18P1 = 18.

After the president is chosen, the number of ways to choose a vice-president from the remaining 17 people is 17P1 = 17.

Similarly, the number of ways to choose a secretary from the remaining 16 people is 16P1 = 16.

Finally, the number of ways to choose a treasurer from the remaining 15 people is 15P1 = 15.

Therefore, the total number of ways to fill these 4 offices is 18P1 * 17P1 * 16P1 * 15P1 = 18 * 17 * 16 * 15 = 73,440.