Multiple choice

In an examination, a student is to choose any 8 questions from a set of 12. If the questions 1 and 3 are compulsory then he can select the questions in

  1. 210 ways

  2. 495 ways

  3. 615 ways

  4. 200 ways
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total questions = 12. Must choose 8. Questions 1 and 3 are fixed, so we must choose 6 more from the remaining 10. Number of ways = 10C6 = 10C4 = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210.

AI explanation

Since questions 1 and 3 are compulsory, the student has already chosen 2 questions and needs to pick 6 more. There are 10 questions remaining from the original 12. The number of ways to choose the remaining 6 questions from the 10 available is given by the combination 10C6. Calculating this gives 10 multiplied by 9 multiplied by 8 multiplied by 7, divided by 4 multiplied by 3 multiplied by 2 multiplied by 1, which equals 210 ways.

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