Question

At an election a voter may vote for any number of candidates not greater than the number to be choosen. There are $10$ candidates and $5$ members are to be chosen. The number of ways in which a voter may vote is

• A. $630$
• B. $632$
• C. $637$
• D. $640$

Answer 1

Answer: (C)

$637$

There are $10$ candidates out of which $5$ members have to be chosen.

And a person can vote up to $5$.

Thus a person can vote either $1,2,3,4$ or $5$ out of $10$.
Hence, required number of ways ${=}^{10}{C}_1{+}^{10}{C}_2{+}^{10}{C}_3{+}^{10}{C}_4{+}^{10}{C}_5=637$