Question

There are 3 candidates and 5 voters. In how many ways can the votes be given? If 3 candidates are among 5 voters and they vote for themselves only, then how many ways of giving votes are possible?

Answer 1

then there are only two votes to be gained
1)one candidate can win both the votes and win
2)there will be three combination in which any two candidates will gain one vote each
so total number of possible outcome is 6

Answer 2

Answer:

First case: Lets take the first voter, he could vote to any 1 of the 3 candidates.

similarly second can vote to any of the 3 candidates... and third and fourth and the fifth...

so total possible ways will be 3 ⨯3⨯ 3 ⨯ 3⨯3 = 35 = 243

Second case:  Assume that the last three person are voter as well as candidate, so they can vote in only one way. And the rest two can give in three ways. So total number of possible was are 3⨯3⨯1⨯1⨯1 = 9 ways