Question

Evaluate 8p5 and 12C4. please show answer step by step.

Answer 1

Hey there :)

8P5 and 12C4

⁸P₅ = is 8! divided by ( 8 - 5 )!

! is called the factorial 
You can see in the picture I have attached of how factorial is calculated

$\frac{8!}{(8-5)!} = \frac{8!}{3!}$

Let us do it separately:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
3! = 3 x 2 x 1 = 6

Let us combine:
$\frac{40320}{6}$ = 6720

¹²C₄ is 12! divided by ( 4! times ( 12 - 4 )! )

$\frac{12!}{(4!(12-4)!)}$ = $\frac{12!}{(4!)(8!)}$

Let us do it separately:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479001600
( 4! )( 8! ) = ( 4 x 3 x 2 x 1 )( 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ) = 24 x 41320 = 967680

Let us combine:
$\frac{478001600}{967680}$ = 495