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

 May 16, 2020
 #1
avatar+29978 
+2

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!

.
 May 16, 2020
edited by Alan  May 16, 2020
 #2
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Alan: Your above calculation is slightly out! : (10 nCr 2)*(8 nCr 3) =2520

 May 16, 2020
 #3
avatar+29978 
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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.

Alan  May 16, 2020
 #4
avatar+57 
+1

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.

 May 16, 2020

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