Step by step
The question
Question: work out 8 P 3.
8P3 =
1 Write the rule
The rule for permutations: n factorial, over n minus r, factorial.
nPr = n!(n − r)!
Here n is 8 and r is 3.
n = 8
r = 3
2 Put the numbers in
We put 8 for n and 3 for r.
8P3 = 8!(8 − 3)!
8 minus 3 is 5.
8P3 = 8!5!
Careful!
The bottom is 8 minus 3, factorial.
Not 3 factorial.
Careful: not 8!3! ✗
3 Write out and cancel
We write every factorial out.
8P3 = 8 × 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 8 × 7 × 6.
8P3 = 8 × 7 × 6
8 times 7 is 56.
56 times 6 is 336.
8 × 7 = 56
56 × 6 = 336
So 8 P 3 is 336.
8P3 = 336
5 Check
8 times 7 times 6 is 336.
The same.
So the answer is right!
8 × 7 × 6 = 336 ✓
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.
Answer
8P3 = 336