In an election a man can vote in 30 ways. If the number of candidates exceeds the number of candidates to be elected by 1, find the number of candidates if a voter has to vote for at least one candidate.

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Solution

$\sum_{k = 1}^{n - 1}^{n} C_{k} = 30$
$o r \sum_{k = 0}^{n}^{n} C_{k} - (^{n} C_{0} +^{n} C_{n})$
or $2^{n}$ = $30 + 2 = 32$ . $∴ n = 5$ .

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In an election a man can vote in 30 ways. If the number of candidates exceeds the number of candidates to be elected by 1, find the number of candidates if a voter has to vote for at least one candidate.

∑n−1k=1nCk=30or∑nk=0nCk−(nC0+nCn)or 2n = 30+2=32.∴n=5.

$\sum_{k = 1}^{n - 1}^{n} C_{k} = 30$
$o r \sum_{k = 0}^{n}^{n} C_{k} - (^{n} C_{0} +^{n} C_{n})$
or $2^{n}$ = $30 + 2 = 32$ . $∴ n = 5$ .