Question

At an election, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. The number of ways in which a voter may vote for at least one candidate is

• A. 385
• B. 1110
• C. 5040
• D. None of these

Answer 1

Answer: (A)

385

Answer 2

Since a voter may choose one, two, three or four candidates out of 10, therefore, the number of ways in which he can vote is $10C_{1} +^{10}C_{2} +^{10}C_{3} +^{10}C_{4}$

= 10 + 45 + 120 + 210

= 385