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Compute $\binom{223}{221}$.

 Jun 18, 2020
 #1
avatar+131 
+2

Another Aops Question...

 

Hint:

\(\binom{n}{k}=\binom{n}{n-k}\)

 Jun 18, 2020
 #2
avatar+732 
+2

\(\dbinom{223}{221}=\dfrac{223!}{221! \cdot2!}=\dfrac{222\cdot223}{2}=111\cdot223=\boxed{24753}\)

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 Jun 18, 2020
 #3
avatar+97 
0

Lol another alcumus question.

Note that \(\binom{n}{k}=\binom{n}{n-k}\) or you could just do it the general way. (Same easy)

 

\(\binom{223}{221}=\binom{223}{2}=\frac{223!}{221!2!} = \frac{223\cdot222}{2}=223\cdot111\)=59393

 

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Note: I may be tricking you! ;)

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This is to prove if you are just here for the answers or not. All these people put lots of time in this and most people just snatch the answers.

 Jun 18, 2020

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