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COMEDK2022MathematicsBinomial Theorem

If ^n C₃=220 , then n= ?

Options

  1. A11
  2. B12
  3. C10
  4. D9

Correct answer

B. 12

Step-by-step solution

The formula for the combination is ^ n C_ r = n! r!(n-r)! . Given ^ n C₃ = 220 , we have n(n-1)(n-2) 3 2 1 = 220 . n(n-1)(n-2) = 220 6 = 1320 . We look for three consecutive integers whose product is 1320 . Testing values: 10 9 8 = 720 11 10 9 = 990 12 11 10 = 1320 . Therefore, n = 12 . Answer: 12

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