Step by step
The question
Question: work out 5 P 3.
5P3 =
1 Write the rule
The rule for permutations: n factorial, over n minus r, factorial.
nPr = n!(n − r)!
Here n is 5 and r is 3.
n = 5
r = 3
2 Put the numbers in
We put 5 for n and 3 for r.
5P3 = 5!(5 − 3)!
5 minus 3 is 2.
5P3 = 5!2!
Careful!
The bottom is 5 minus 3, factorial.
Not 3 factorial.
Careful: not 5!3! ✗
3 Write out and cancel
We write every factorial out.
5P3 = 5 × 4 × 3 × 2 × 12 × 1
2 times 1 is on top and at the bottom.
They cancel.
4 Multiply
What is left is 5 × 4 × 3.
5P3 = 5 × 4 × 3
5 times 4 is 20.
20 times 3 is 60.
5 × 4 = 20
20 × 3 = 60
So 5 P 3 is 60.
5P3 = 60
5 Check
5 times 4 times 3 is 60.
The same.
So the answer is right!
5 × 4 × 3 = 60 ✓
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.
Answer
5P3 = 60