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Question
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
Solution
Given question n has n + 1 choices
question 1 has 1 + 1 = 2 choices
question 2 has 2 + 1 = 3 choices
question 3 has 3 + 1 = 4 choices
question 4 has 4 + 1 = 5 choices
question 5 has 5 + 1 = 6 choices
question 6 has 6 + 1 = 7 choices
question 7 has 7 + 1 = 8 choices
question 8 has 8 + 1 = 9 choices
question 9 has 9 + 1 = 10 choices
So the number of ways of answering all the 10 questions
= 2 × 3 × 4 × …. × 11
= 11! ways
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