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0
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avatar+586 

compute\(\dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4}\)

 Oct 21, 2018
 #1
avatar+128 
+1

Well,

4 choose 0 = 1,

4 choose 1 = 4,

4 choose 2 = 6,

4 choose 3 = 4 choose 1 = 4,

4 choose 4 = 4 choose 0 = 1,

1+4+6+4+1 = 16

 

16, and good luck!

 Oct 21, 2018
 #2
avatar+21848 
+9

compute:

\(\dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4}\)

 

\(\begin{array}{|rcll|} \hline (1+1)^4 &=& \dbinom{4}{0}\cdot 1^4\cdot 1^0 + \dbinom{4}{1}\cdot 1^3\cdot 1^1 + \dbinom{4}{2}\cdot 1^2\cdot 1^2 + \dbinom{4}{3}\cdot 1^1\cdot 1^3 + \dbinom{4}{4}\cdot 1^0\cdot 1^4 \\\\ (1+1)^4 &=& \dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4} \\\\ 2^4 &=& \dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4} \\\\ 16 &=& \dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4} \\ \hline \end{array}\)

 

laugh

 Oct 22, 2018

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