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

Explanation

The values are C(10,3)=120, C(10,4)=210, C(10,5)=252, C(10,6)=210, and C(10,7)=120. The harmonic mean (HM) of n numbers is n / \sum (1/x_i). The sum of their reciprocals is \frac{2}{120} + \frac{2}{210} + \frac{1}{252} = \frac{1}{60} + \frac{1}{105} + \frac{1}{252}. Using LCM 1260, this is \frac{21 + 12 + 5}{1260} = \frac{38}{1260} = \frac{19}{630}. Thus, HM = \frac{5}{19/630} = \frac{3150}{19}.

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