Permutation Math Example 3

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

Example 3

easy

How many

4

-digit PIN codes can be formed using the digits

\{1,2,3,4,5,6\}

if no digit may be repeated?

Solution

1
This is a permutation of $4$ items from $6$ : $P(6,4) = \frac{6!}{2!} = \frac{720}{2} = 360$ .
2
Alternatively: $6 \times 5 \times 4 \times 3 = 360$ .

Answer

360

Since the order of digits in a PIN matters and repetition is not allowed, this is a straightforward permutation problem.

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 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 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