Permutation Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A club of 88 students must choose a president, vice president, and secretary. In how many ways can the officers be chosen?

Solution

  1. 1
    The positions are different, so order matters.
  2. 2
    Use permutations: P(8,3)=8!(8−3)!=8!5!P(8, 3) = \frac{8!}{(8-3)!} = \frac{8!}{5!}.
  3. 3
    Simplify: 8×7×6=3368 \times 7 \times 6 = 336.

Answer

336336
Officer roles are distinct, so choosing one student for president and another for secretary is a different outcome from swapping them. That is why permutations apply instead of combinations.

About Permutation

A permutation is an ordered arrangement of objects — the number of ways to choose and order rr items from nn distinct items is P(n,r)=n!(n−r)!P(n,r) = \frac{n!}{(n-r)!}.

Learn more about Permutation →

More Permutation Examples

Example 1 easy

In how many ways can [formula] students be arranged in a line from a group of [formula]?

Example 2 medium

How many distinct arrangements of the letters in the word MISSISSIPPI are there?

Example 3 easy

How many [formula]-digit PIN codes can be formed using the digits [formula] if no digit may be repea

← All Permutation Examples Permutation Concept

Related Concepts

FactorialCombination