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penfila11Pen
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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

[tex] \frac{8!}{(8-5)!} = \frac{8!}{3!} [/tex]

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:
[tex] \frac{40320}{6}[/tex] = 6720

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

[tex] \frac{12!}{(4!(12-4)!)} [/tex] = [tex] \frac{12!}{(4!)(8!)} [/tex]

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:
[tex] \frac{478001600}{967680} [/tex] = 495

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