How do I solve 65!/63!(65-63)!?

65!/63!(65-63)!

Since 65! is on top and 63! is on the bottom you are basically able to cancel the numbers 1*2*3*4....*63 out since they're on the bottom and top. Leaving 64*65 on top = 4160

Thus,

4160/(65-63)! = 4160/2! = 4160/2 = 2080.

65! = 65 x 64 x 63 x 62 x... x 1

63! = 63 x 62 x 61 x.... x 1

so 65!/63! ends up being just 65 x 64 = 4160

(65 - 63)! is 2! = 2 x 1 = 2

From the answer, I guess that the (65-63)! is meant to be part of the division

4160/2 = 2080

65! is also equal to 65*64*(63!)

So 63! cancels out, and you will be left with (65*64)/(65-63)!

But (65-63)! is also equal to (2)!

So you will be left with (65*64)/2

Which is equal to 2080

n! means (n)(n-1)(n-2)... (3)(2)(1). You can write this as [(n)(n-1)](n-2)!, so 65! = (65)(64)(63!). Thus:

65!/63!(65-63)!

(65)(64)(63!)/(63!)(2!) (simplify)

(65)(64)/2 (cancel)

65×32 = 2,080