factorials???

Question

i cant understand my math teacher and i have no idea how to solve for factorial division with 2 #s at the bottom. so can someone explain how you solve it step by step. an example would be 15!/3! 8!

Answer 1

Presumably you understand what a factorial is, 15!= 15 x 14 x 13 .... x 1.

The denominator here is just 3! x 8!

The problem is then layed out like below

15x14x13x12x11x10x9x8x7x6x5x4x3x2x1
-----------------------------------
3x2x1 x 8x7x6x5x4x3x2x1

By crossing out factors that appear both in the numerator and denominator the problem is reduced to

15x14x13x12x11x10x9
-------------------
3x2x1

This you should be able to do on your calculator.

Answer 2

I'm kinda guessing here that you mean 15!/(3!*8!)
Take it one piece at a time. 15!/8! is just
15*14*13*12*11*10*9 and all of the other terms (8 through 1) divide out. Now notice that in 3! there's a 3 and a 2. The three divides the 9 3 times and the 2 divides the 10 5 times so hte final answer is
15*14*13*12*11*5*3 = (3*5)*(15!/10!) = 24024

HTH

Doug

Answer 3

x! = 1*2*3*4*5*6*7*8*9........till x
now 15!/3!8!=1*2*3*4*5*6*7*8*9*10*11*12*13*14*15/(1*2*3)(1*2*3*4*5*6*7*8)

now 1*2*3*4*5*6*7*8 is common both in numerator & denominator so what remains is 9*10*11*12*13*14*15/1*2*3=
9*10*11*2*13*14*15 (12/6 = 2)
= 5405400