Step by step
The question
Question: work out 7 P 3.
7P3 =
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 3.
n = 7
r = 3
2 Put the numbers in
We put 7 for n and 3 for r.
7P3 = 7!(7 − 3)!
7 minus 3 is 4.
7P3 = 7!4!
Careful!
The bottom is 7 minus 3, factorial.
Not 3 factorial.
Careful: not 7!3! ✗
3 Write out and cancel
We write every factorial out.
7P3 = 7 × 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 7 × 6 × 5.
7P3 = 7 × 6 × 5
7 times 6 is 42.
42 times 5 is 210.
7 × 6 = 42
42 × 5 = 210
So 7 P 3 is 210.
7P3 = 210
5 Check
7 times 6 times 5 is 210.
The same.
So the answer is right!
7 × 6 × 5 = 210 ✓
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: write out and cancel.
Then: multiply.
Last: check.
Answer
7P3 = 210