Step by step
The question
Question: work out 7 P 2.
7P2 =
1 Write the rule
The rule for permutations: n factorial, over n minus r, factorial.
nPr = n!(n − r)!
Here n is 7 and r is 2.
n = 7
r = 2
2 Put the numbers in
We put 7 for n and 2 for r.
7P2 = 7!(7 − 2)!
7 minus 2 is 5.
7P2 = 7!5!
Careful!
The bottom is 7 minus 2, factorial.
Not 2 factorial.
Careful: not 7!2! ✗
3 Write out and cancel
We write every factorial out.
7P2 = 7 × 6 × 5 × 4 × 3 × 2 × 15 × 4 × 3 × 2 × 1
5 times 4 times 3 times 2 times 1 is on top and at the bottom.
They cancel.
4 Multiply
What is left is 7 × 6.
7P2 = 7 × 6
7 times 6 is 42.
7 × 6 = 42
So 7 P 2 is 42.
7P2 = 42
5 Check
7 times 6 is 42.
The same.
So the answer is right!
7 × 6 = 42 ✓
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.
Answer
7P2 = 42