Step by step
The question
Question: work out 9 P 2.
9P2 =
1 Write the rule
The rule for permutations: n factorial, over n minus r, factorial.
nPr = n!(n − r)!
Here n is 9 and r is 2.
n = 9
r = 2
2 Put the numbers in
We put 9 for n and 2 for r.
9P2 = 9!(9 − 2)!
9 minus 2 is 7.
9P2 = 9!7!
Careful!
The bottom is 9 minus 2, factorial.
Not 2 factorial.
Careful: not 9!2! ✗
3 Write out and cancel
We write every factorial out.
9P2 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 17 × 6 × 5 × 4 × 3 × 2 × 1
7 times 6 times 5 times 4 times 3 times 2 times 1 is on top and at the bottom.
They cancel.
4 Multiply
What is left is 9 × 8.
9P2 = 9 × 8
9 times 8 is 72.
9 × 8 = 72
So 9 P 2 is 72.
9P2 = 72
5 Check
9 times 8 is 72.
The same.
So the answer is right!
9 × 8 = 72 ✓
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.
Answer
9P2 = 72