Question

At an election there are five candidates and three members to be elected , and a voter may vote for any number of candidates not greater than the number to be elected. then the number of ways in which a voter may vote is

Answer 1

Ans. is 25
solution is in the pic....

Answer 2

Given,

Total candidates to be elected = 5

Total members to be elected = 3

To Find,

the number of ways in which a voter may vote if the voter may vote for any number of candidates not greater than the number to be elected =?

Solution,

If voters vote for 3 candidates = 5C3 = 5! / (3!*2!)

If voters vote for 3 candidates =  10

If voters vote for 2 candidates = 5C2 = 5! / (3! * 2!) = 10

If voters vote 1 candidate = 5C1 = 5! / (4! * 1!) = 5

Total ways = 5C3 + 5C2 +5C

Total ways = 10 + 10 +5 = 25

Hence, the number of ways in which a voter may vote if the voter may vote for any number of candidates not greater than the number to be elected is 25 ways.