Question

In a n election, the number of candidates exceeds the number to be elected y 2. A man can vote in 56 ways. Find the number of candidates.

Answer 1

Correct Answer - 6
Let the number of candidates be n. Therefore, (n-2) are to be elected and so one can vote up to n-2. Hence, the number of ways in which one can vote is
`.^(n)C_(1)+ .^(n)C_(2)+..+ .^(n)C_(n-2)=56` (given)
or `2^(n)-(.^(n)C_(n-1)+ .^(n)C_(n))=56`
or `2^(n)-n=58`
or `2^(n)=58+n`
which is satisfied by n =6 only.