Multiple choice

The number of different ways of distributing 10 marks among 3 questions, each carrying at least 1 mark, is

  1. $72$
  2. $71$
  3. $36$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a stars and bars problem. Distribute 10 marks into 3 questions with at least 1 mark each. Let x1+x2+x3=10, where xi >= 1. Let yi = xi-1, so y1+y2+y3 = 10-3 = 7. Number of ways = C(n+k-1, k-1) = C(7+3-1, 3-1) = C(9, 2) = 36.

AI explanation

To distribute 10 marks among 3 questions with each carrying at least 1 mark, assign 1 mark to each question first, leaving 7 marks to be distributed freely. Using the stars and bars method, the formula is (n + r - 1) C (r - 1), where n is the remaining marks and r is the number of questions. This results in (7 + 3 - 1) C (3 - 1), which is 9 C 2, yielding 36.

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