Question

The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president. In how many ways can this promotion be made?

Answer 1

720 ways

The number of ways in which the promotion can be made is 720 ways

Explanation:

Given that;

The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president.

This is a permutation problem because the order of selection is relevant. They will be promoted to various positions.

N = nPr = n!/(n-r)!

n = 10, r = 3

Substituting the values;

N = 10P3

N = 10!/(10-3)! = 10!/7!

N = 720 ways

The number of ways in which the promotion can be made is 720 ways