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avatar+42 

 

Compute \( \binom40+\binom51+\binom62+\binom73.\)

I'm not sure how to solve these binomial expressions.

 Apr 9, 2019
 #1
avatar+6046 
+2

\(\dbinom{n}{k} = \dfrac{n!}{k!(n-k)!}\\ n! = n \cdot (n-1) \cdot (n-2) \cdot \dots \cdot 3 \cdot 2\)

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 Apr 9, 2019
 #2
avatar+42 
0

Thanks!

detkitten  Apr 9, 2019
 #3
avatar+106519 
+3

Note that

 

C(n,m) + C(n + 1, m + 1) + C(n + 2, m + 2)  + .....+ C( n + q, m + q)  =  C (n + q + 1, m + q)

 

So

 

C(4,0)  + C(5, 1) + C(6,2) + C(7, 3)  = C(8, 3)   =   56

 

 

cool cool cool

 Apr 9, 2019

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