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

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(A) Given $n = ^mC_2 = \frac{m(m-1)}{2}$.We need to find $^nC_2 = \frac{n(n-1)}{2}$.Substituting $n = \frac{m(m-1)}{2}$:$^nC_2 = \frac{\frac{m(m-1)}{2} \left( \frac{m(m-1)}{2} - 1 \right)}{2}$$= \frac{\frac{m(m-1)}{2} \left( \frac{m^2-m-2}{2} \right)}{2}$$= \frac{m(m-1)(m^2-m-2)}{8}$$= \frac{m(m-1)(m-2)(m+1)}{8}$$= \frac{3 \times (m+1)m(m-1)(m-2)}{4 \times 3 \times 2 \times 1}$$= 3(^{m+1}C_4)$.

Class 11 Mathematics Permutation and Combination Mix Examples-Permutation and Combination

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

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$3(^{m+1}C_4)$
B
$^{m-1}C_4$
C
$^{m+1}C_4$
D
$2(^{m+2}C_4)$

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

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