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What is the harmonic mean of the numbers C(10, 3) , C(10, 4) , C(10, 5) , C(10, 6) and C(10, 7) ?

Options

  1. A3150/19
  2. B4000/19
  3. C252
  4. D225

Correct answer

A. 3150/19

Step-by-step solution

The given numbers are ¹⁰C₃ , ¹⁰C₄ , ¹⁰C₅ , ¹⁰C₆ , and ¹⁰C₇ . Calculating their values: ¹⁰C₃ = 10 9 8 3 2 1 = 120 ¹⁰C₄ = 10 9 8 7 4 3 2 1 = 210 ¹⁰C₅ = 10 9 8 7 6 5 4 3 2 1 = 252 ¹⁰C₆ = ¹⁰C₄ = 210 ¹⁰C₇ = ¹⁰C₃ = 120 The harmonic mean H of n numbers x₁, x₂, , x_n is given by: H = n 1 x₁ + 1 x₂ + + 1 x_n Here n = 5 . The sum of the reciprocals is: S = 1 120 + 1 210 + 1 252 + 1 210 + 1 120 S = 2 120 + 2 210 + 1 252 S = 1 60 + 1 105 + 1 252 Taking the LCM of 60, 105, 252 , which is 1260 : S = 21 + 12 + 5 1260 = 38 1260 =

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