Step by step
The question
Question: work out 6 P 3.
6P3 =
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 3.
n = 6
r = 3
2 Put the numbers in
We put 6 for n and 3 for r.
6P3 = 6!(6 − 3)!
6 minus 3 is 3.
6P3 = 6!3!
Careful!
The bottom is 6 minus 3, factorial.
Not 3 factorial.
Careful: not 6!3! ✗
3 Write out and cancel
We write every factorial out.
6P3 = 6 × 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 6 × 5 × 4.
6P3 = 6 × 5 × 4
6 times 5 is 30.
30 times 4 is 120.
6 × 5 = 30
30 × 4 = 120
So 6 P 3 is 120.
6P3 = 120
5 Check
6 times 5 times 4 is 120.
The same.
So the answer is right!
6 × 5 × 4 = 120 ✓
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.
Answer
6P3 = 120