If n = ^mC_2, then the value of ^nC_2 is give | vedclass

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(A) Given $n = ^mC_2 = \frac{m(m-1)}{2}$.We need to find the value of $^nC_2 = \frac{n(n-1)}{2}$.Substituting the value of $n$:$^nC_2 = \frac{\frac{m(

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$3(^{m+1}C_4)$

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(A) Given $n = ^mC_2 = \frac{m(m-1)}{2}$.We need to find the value of $^nC_2 = \frac{n(n-1)}{2}$.Substituting the value of $n$:$^nC_2 = \frac{\frac{m(m-1)}{2} \left( \frac{m(m-1)}{2} - 1 ight)}{2}$$= \frac{\frac{m(m-1)}{2} \left( \frac{m^2 - m - 2}{2} ight)}{2}$$= \frac{m(m-1)(m^2 - m - 2)}{8}$Factorizing $(m^2 - m - 2)$ as $(m-2)(m+1)$:$= \frac{m(m-1)(m-2)(m+1)}{8}$Rearranging the terms:$= \frac{(m+1)m(m-1)(m-2)}{8}$To express this in terms of combinations,multiply and divide by $3! = 6$:$= \frac{6}{8} 	imes \frac{(m+1)m(m-1)(m-2)}{3 	imes 2 	imes 1}$$= \frac{3}{4} 	imes ^{m+1}C_4$Wait,re-evaluating the expression:$= \frac{(m+1)m(m-1)(m-2)}{8} = 3 	imes \frac{(m+1)m(m-1)(m-2)}{24} = 3(^{m+1}C_4)$.

If $n = ^mC_2,$ then the value of $^nC_2$ is given by

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