Question

At an election, a voter may vote for any number of candidates not exceeding the number to be elected. If 4 candidates are to be elected out of the 12 contested in the election and voter votes for at least one candidate, then the number of ways of selections is:

• A. 793
• B. 298
• C. 781
• D. 1585

Hint:

For combinations, use the formula \( ^nC_r = \frac{n!}{r!(n-r)!} \) to calculate the number of ways to choose \( r \) objects from \( n \) objects.

Answer 1

The Correct Option is A

The problem requires calculating the number of combinations for selecting one to four candidates from a pool of twelve. This is achieved by summing the combinations for each selection size: selecting 1 candidate (C(12,1) = 12), selecting 2 candidates (C(12,2) = 66), selecting 3 candidates (C(12,3) = 220), and selecting 4 candidates (C(12,4) = 495). The total number of ways to select at least one candidate is the sum of these possibilities: 12 + 66 + 220 + 495 = 793.

Therefore, there are 793 distinct ways for voters to select candidates.