# Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?

A. 9

B. 30

C. 36

D. 15

**Answer: Option D **

__Solution(By Examveda Team)__

There are 6 candidates and a voter has to vote for any two of them.So, the required number of ways is,

$$\eqalign{ & { = ^6}{{\text{C}}_2} \cr & = \frac{{6!}}{{2! \times 4!}} \cr & = 15 \cr} $$

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## Comments ( 4 )

Related Questions on Permutation and Combination

A. 3! 4! 8! 4!

B. 3! 8!

C. 4! 4!

D. 8! 4! 4!

A. 7560,60,1680

B. 7890,120,650

C. 7650,200,4444

D. None of these

A. 8 × 9!

B. 8 × 8!

C. 7 × 9!

D. 9 × 8!

I feel that the answer is wrong

since after casting 1 vote, he has 5 candidates to choose from

so the answer should be 30 (6C1*5C1)

as per the solution given the person is straightaway choosing 2 people out of 6 which is wrong.

this is wrong.! There will be 30 different ways to vote.

M1M2, M1M3, M2M1, M2M3, M3M1, M3M2

W1W2, W1W3, W2W1, W2W3, W3W1, W1W2,

W1M1, W1M2,W1M3, W2M1, W2M2,W2M3,

W3M1, W3M2,W3M3, M1W1, M1W2, M1W3,

M2W1, M2W2, M2W3, M3W1, M3W2, M3W3

1 gentlemen and(*) 1 lady or (+) 2 gentleman

or(+) 2 ladies =

=3c1*3c1 + 3c2 +3c2

=9+6+6

=15

WHY TAKE 4! ?