Step by step
The question
Question: work out 6 P 2.
6P2 =
1 Write the rule
The rule for permutations: n factorial, over n minus r, factorial.
nPr = n!(n − r)!
Here n is 6 and r is 2.
n = 6
r = 2
2 Put the numbers in
We put 6 for n and 2 for r.
6P2 = 6!(6 − 2)!
6 minus 2 is 4.
6P2 = 6!4!
Careful!
The bottom is 6 minus 2, factorial.
Not 2 factorial.
Careful: not 6!2! ✗
3 Write out and cancel
We write every factorial out.
6P2 = 6 × 5 × 4 × 3 × 2 × 14 × 3 × 2 × 1
4 times 3 times 2 times 1 is on top and at the bottom.
They cancel.
4 Multiply
What is left is 6 × 5.
6P2 = 6 × 5
6 times 5 is 30.
6 × 5 = 30
So 6 P 2 is 30.
6P2 = 30
5 Check
6 times 5 is 30.
The same.
So the answer is right!
6 × 5 = 30 ✓
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.
Answer
6P2 = 30