If a club consists of 11 members, how many different arrangements of president, vice-president, and secretary are possible?

Because 1 person is now the president, there are only 10 people left who are candidates for vice-president. Therefore, there are only 10 ways to choose the vice-president.

Because 1 person is president and another is vice-president, out of those 11 members, there are now only 9 people who can be candidates for secretary. Therefore, there are 9 ways to choose the secretary.

Multiply the ways to choose a president, vice-president, and secretary out of 11 club members, and you get:

11 * 10 * 9 = 990 (ways)

MrRoyal MrRoyal · Answer 2 · 2022-04-28T12:20:16+02:00

There are 990 different arrangements of president, vice-president, and secretary

The number of arrangements

The given parameters are:

Club members, n = 11

Members to arrange, r = 3

The number of arrangements is calculated using the following permutation equation

Ways = nPr

This gives

Ways = 11P3

Evaluate

Ways = 990

Hence, there are 990 different arrangements of president, vice-president, and secretary