+1206 compute\(\dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4}\)
+127 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!
+26367 compute:
\(\dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4}\)
\(\begin{array}{|rcll|} \hline (1+1)^4 &=& \dbinom{4}{0}\cdot 1^4\cdot 1^0 + \dbinom{4}{1}\cdot 1^3\cdot 1^1 + \dbinom{4}{2}\cdot 1^2\cdot 1^2 + \dbinom{4}{3}\cdot 1^1\cdot 1^3 + \dbinom{4}{4}\cdot 1^0\cdot 1^4 \\\\ (1+1)^4 &=& \dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4} \\\\ 2^4 &=& \dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4} \\\\ 16 &=& \dbinom{4}{0}+\dbinom{4}{1}+\dbinom{4}{2}+\dbinom{4}{3}+\dbinom{4}{4} \\ \hline \end{array}\)
