Step by step
The question
Question: How many ways can 4 of 6 books be put in a row on a shelf?
1 Order: yes or no
Does order matter?
Book A then book B is a different row from book B then book A.
So order matters.
That is called a permutation.
2 Write the rule
The rule for permutations: n factorial, over n minus r, factorial.
n is how many we choose from: 6.
r is how many we put in order: 4.
3 Put the numbers in
We put 6 for n and 4 for r.
6 minus 4 is 2.
Careful!
The bottom is 6 minus 4, factorial.
Not 4 factorial.
4 Write out and cancel
We write every factorial out.
2 times 1 is on top and at the bottom.
They cancel.
5 Multiply
What is left is 6 × 5 × 4 × 3.
6 times 5 is 30.
30 times 4 is 120.
120 times 3 is 360.
So there are 360 ways.
6 Check
6 times 5 times 4 times 3 is 360.
The same.
So the answer is right!
Let's look back.
First: order: yes or no.
Then: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.