Permutation Math Example 1

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

Example 1

easy

In how many ways can

3

students be arranged in a line from a group of

7

Solution

1
Recall the permutation formula for ordered selections: $P(n, r) = \frac{n!}{(n-r)!}$ , where $n = 7$ and $r = 3$ .
2
Expand the factorial ratio: $P(7, 3) = \frac{7!}{(7-3)!} = \frac{7!}{4!} = 7 \times 6 \times 5$
3
Calculate the product: $7 \times 6 \times 5 = 210$

Answer

P(7,3) = 210

Permutations count ordered arrangements. Since the order in a line matters (ABC differs from BAC), we use permutations rather than combinations.

About Permutation

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

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More Permutation Examples

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

Example 4 medium

A club of [formula] students must choose a president, vice president, and secretary. In how many way

← All Permutation Examples Permutation Concept

Related Concepts

Factorial Combination