Question

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ___

Answer 1

The number of ways in which a candidate answers all six questions such that exactly four of the answers are correct is 90.

Step-by-step explanation:

The number of ways in which a candidate answers all six questions such that exactly four of the answers are correct can be calculated using combination formula. We can choose 4 questions out of 6 to be correct, and for each of these 4 questions, there is only one correct answer out of the 4 alternatives. So, the number of ways is given by:

1. (6 choose 4) * (1 choose 1) * (4 choose 2)
2. = 15 * 1 * 6
3. = 90

The number of ways in which a candidate answers all six questions such that exactly four of the answers are correct is 90.