If $^{n}C{8} = ^{n}C{2}$, then find the value of $^{n}C{3}$.

Question

Accepted Answer

Since $^{n}C{8} = ^{n}C{2}$, we have $n = 8 + 2 = 10$. Now, calculate $^{10}C{3} = \frac{10!}{3!7!} = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$. Thus, option A is correct.

Permutations and Combinations

❓ Sibling Questions in this Chapter