Evaluate the expression. C(8, 6) · C(7, 5) /C(9, 5)

Answer 1

I'll assume no calculator is allowed to solve this so I will show you by hand:

8!/(6!(8-6)!) * 7!/(5!(7-5)!) / (9!/(5!(9-5)!))

8*7*6!/(6!*2) * 7*6*5!/(5!*2) * 5!*4*3*2/(9*8*7*6*5!)

Divide out the factorials (dividing by a fraction is the same as multiplying by its reciprocal if youre confused by the last piece)

8*7/2 * 7*6/2 *4*3*2/(9*8*7*6)

Now simplify among fractions

4*7 * 7*3 / (3*7*6)

Combine and continue to simplify

2*7/3 = 14/3