?
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?
Answer & Solution
Correct Answer:
Option
D
There are 6 candidates and a voter has to vote for any two of them. So, the required number of ways is,
$$\eqalign{
& { = ^6}{{\text{C}}_2} \cr
& = \frac{{6!}}{{2! \times 4!}} \cr
& = 15 \cr} $$
Join the Discussion
Login to post a comment or share your explanation.
Loginsince 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.
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
or(+) 2 ladies =
=3c1*3c1 + 3c2 +3c2
=9+6+6
=15