A) 5
B) 6
C) 7
D) 8
Correct Answer: B
Solution :
Let number of candidates be n. Therefore,\[n-2\] are to be elected and so one can vote up to\[(n-2)\]. Hence, .number of ways in which one can vote \[{{=}^{n}}{{C}_{1}}{{+}^{n}}{{C}_{2}}+...{{+}^{n}}{{C}_{n-2}}=56\](given) \[\Rightarrow \] \[{{2}^{n}}-{{(}^{n}}{{C}_{0}}{{+}^{n}}{{C}_{n-1}}{{+}^{n}}{{C}_{n}})=56\] \[\Rightarrow \] \[{{2}^{n}}-n=58\,\,\,\Rightarrow \,\,\,{{2}^{n}}=58+n\] Which is satisfied by\[n=6\]only.
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