Question

Each of 5 questions in a multiple choice questions test has four alternatives of which one or more are correct. If a candidate ticks at least one alternative in answering each question, the number of different sets of possible answers is

• A. 4^5
• B. (15)^5
• C. 15 x 5
• D. 5^4

Answer 1

Answer: (B)

(15)^5

Answer 2

A candidate may tick one, two, three or all the four

alternatives. So, he can answer one question in

$4C_{1} +^{4}C_{2} +^{4}C_{3} +^{4}C_{4}$

= 4 + 6 + 4 + 1 = 15 ways.

Hence all the five questions can be answered in

15 x 15 x 15 x 15 x 15 = (15)⁵ ways.