Step by step
The question
Question: work out 5 P 2.
5P2 =
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 2.
n = 5
r = 2
2 Put the numbers in
We put 5 for n and 2 for r.
5P2 = 5!(5 − 2)!
5 minus 2 is 3.
5P2 = 5!3!
Careful!
The bottom is 5 minus 2, factorial.
Not 2 factorial.
Careful: not 5!2! ✗
3 Write out and cancel
We write every factorial out.
5P2 = 5 × 4 × 3 × 2 × 13 × 2 × 1
3 times 2 times 1 is on top and at the bottom.
They cancel.
4 Multiply
What is left is 5 × 4.
5P2 = 5 × 4
5 times 4 is 20.
5 × 4 = 20
So 5 P 2 is 20.
5P2 = 20
5 Check
5 times 4 is 20.
The same.
So the answer is right!
5 × 4 = 20 ✓
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.
Answer
5P2 = 20