There are 6 multiple choice questions in an examination. How many sequences of answers are possible if the first three questions have 4 choices each and next three have 5 each ?
Given: There are 6 multiple choice questions such that first three questions have 4 choices each and next three have 5 choices each. Here, we have to find the number of possible sequence of answers. ∵ The first three questions have 4 choices in each. So, each of the first three questions can be answered in 4 ways. So, the possible sequence of answers in which the first three questions can be answered = 4 × 4 × 4 = 64 ∵ The next three questions have 5 choices in each. So, each of the next three questions can be answered in 5 ways. So, the possible sequence of answers in which the next three questions can be answered = 5 × 5 × 5 = 125 Hence. the total number of possible sequence of answers = 64 × 125 = 8000