## anonymous 4 years ago probability(choosing) question: if (5C0)+(5C1)+(5C2)+(5C3)+(5C4)+(5C3)=2^k, find k.

1. anonymous

$If\left(\begin{matrix}5 \\ 0\end{matrix}\right)+\left(\begin{matrix}5 \\ 1\end{matrix}\right)+\left(\begin{matrix}5 \\ 2\end{matrix}\right)+\left(\begin{matrix}5 \\ 3\end{matrix}\right)+\left(\begin{matrix}5 \\ 4\end{matrix}\right)+\left(\begin{matrix}5 \\ 3\end{matrix}\right) = 2^{k}, find k$

2. phi

isn't the last term 5C5 ? otherwise you don't get an even number. to solve, simplify the terms on the left to numbers, add them up, and expects a power of 2. For example 5C0= 1. continue for 5C1, etc

3. anonymous

nope, in book is 5C3 (the last one) prolly miss print then i guess =/

4. anonymous

$\sum_{c=0}^{6}{\left(\begin{matrix}5 \\ c\end{matrix}\right)}=2^k$ $32=2^k\rightarrow 2^5=2^k$ k=5

5. anonymous

0_o

6. anonymous

If last term isn't 5C5 then k=5.39232