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6.Permutation and Combination
medium
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are $10$ candidates and $4$ are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is
A
$5040$
B
$6210$
C
$385$
D
$1110$
(AIEEE-2006)
Solution
No. of candidates $=10$
A voter can vote at the most $4$ candidates and alteast one candidate.
No. of ways in which he can vote for $1$ candidate $=^{10}C_{1}=10$
No. of ways in which he can vote for $2$ candidate $=^{10}C_{2}=45$
No. of ways in which he can vote for $3$ candidate $=^{10}C_{3}=120$
No. of ways in which he can vote for $4$ candidate $=^{10}C_{4}=210$
The required no. of ways $=10+45+120+210=385$
Standard 11
Mathematics
