Compute \(\dbinom{10}{2}*\dbinom{8}{3}\).

As follows:

\(\frac{10!}{2!(10-2)!}\times \frac{8!}{3!(8-3)!}= \frac{10!}{2!}\times \frac{1}{3!5!}=\frac{10*9*8*7*6}{2*6}=2520\)

Edited to correct silly error!

Alan: Your above calculation is slightly out! : (10 nCr 2)*(8 nCr 3) =2520

Oops! Thank you, you are correct. I've kept a 5! in the denominator, after I'd cancelled it with part of the 10! in the numerator. I'll change it.

10 choose 2 is 45 because 10!/(10-2)!*2 equals 10!/8!*2 10!/8! is 90 90 divided by 2 is 45. 8 choose 3 is 56. 45*56 is 2520 so the answer is 2520.