Permutations

Order matters for Permutations.

How many ways can we order 3 numbers $(1,2,3)$? There are 6 ways.

• 1 - 2 - 3
• 1 - 3 - 2
• 2 - 1 - 3
• 2 - 3 - 1
• 3 - 1 - 2
• 3 - 2 - 1

The number of ways is just $n!$

Quick explanation: How many ways can we select the number in the first position, we have 3. Now we have 2 options for the second position. Similarly, only 1 choice for the third position.

ways $= 3 * 2 * 1 = 3! = 6$ ...