CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
If nC2 = 45, find the value of n.
The value of n is 10. Since nC2 = n(n-1)/2 = 45, we get n(n-1) = 90, which is satisfied by n = 10 because 10 × 9 = 90. Verifying, 10C2 = 45, so the other values do not fit.
- A9
- B10Correct
- C11
- D12
Explanation
nC2 = n(n-1)/2 = 45 gives n(n-1) = 90, so n = 10 since 10×9 = 90. Check: 10C2 = 45. Option 9 gives 36 and 11 gives 55.
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