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

This Question Belongs to Arithmetic Ability >> Permutation And Combination

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Comments ( 4 )

  1. 2K18/ME/192 SANCHIT
    2K18/ME/192 SANCHIT :
    3 years ago

    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.

  2. Noah Johnson
    Noah Johnson :
    6 years ago

    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

  3. Juhi Shah
    Juhi Shah :
    7 years ago

    1 gentlemen and(*) 1 lady or (+) 2 gentleman
    or(+) 2 ladies =
    =3c1*3c1 + 3c2 +3c2

  4. Mrunali Gedam
    Mrunali Gedam :
    9 years ago

    WHY TAKE 4! ?

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