If a=mC2 ,then find the value of aC2 - Maths - Permutations and Combinations

Question

If a=mC2 ,then find the value of
aC2

Aakash Sharma · Accepted Answer

Given : a = mC2 = $\frac{m!}{2! \times (m - 2)!} = \frac{m (m - 1) (m - 2)!}{2 \times (m - 2)!} = \frac{m (m - 1)}{2}$ Thus, ${}^{a}{C_{2}} = \frac{a!}{2! \times (a - 2)!} = \frac{a (a - 1) (a - 2)!}{2 \times (a - 2)!} = \frac{a (a - 1)}{2} = \frac{(\frac{m (m - 1)}{2}) (\frac{m (m - 1)}{2} - 1)}{2} = \frac{m (m - 1) (m^{2} - m - 2)}{8}$

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