ShmoopTube

00:02

Here’s your shmoop du jour, brought to you by Permutations.

00:06

The preferred hairstyle of mathematicians.

00:09

Six students are arranged in a row.

00:12

How many different ways can this happen? And here are the potential answers…

00:18

When we are arranging students in a row, we are counting permutations.

00:26

The easy way to solve one of these permutation problems is

00:28

to simply take the factorial of the number we are ordering.

00:35

In this case…it's 6.

00:37

We start with 6 spaces to place the students.

00:41

When we go to place the first student, we have 6 to choose from.

00:45

Then, for our next slot, there are only 5 left.

00:47

With each successive space, there is one less

00:50

choice, since another was used up in the previous slot.

00:54

Now, to find the possible permutations of students, we simply multiply the number of

00:58

choices for all slots together.

01:01

Which equals 720, that's 6 factorial.

01:04

So we get 720 possible outcomes. Our answer is just (C).

Full Transcript