JEE Main · 2006 · 30 Apr 2006 · Offline · Permutations and Combinations

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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 elected. 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✓ Correct
(D)1110

Answer: (C)

Solution

A voter may mark one, two, three or four names chosen from the ten candidates, and the order of marking does not matter, so each case is a combination. The counts are

(1 10) = 10

(2 10) = 45

(3 10) = 120

and

(4 10) = 210

. Adding them,

10 + 45 + 120 + 210 = 385

, which is the number of ways to cast a valid vote.

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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