A sports team of $$11$$ students is to be constituted, choosing at least $$5$$ from class $$XI$$ and at least $$5$$ from class $$XII$$. If there are $$20$$ students in each of these classes, in how many ways can the teams be constituted?
A
$$2(\ ^{20}C_{5}\times \ ^{20}C_{6})$$
B
$$2(\ ^{20}C_{3}\times \ ^{20}C_{7})$$
C
$$2(\ ^{20}C_{4}\times \ ^{20}C_{8})$$
Correct option is B. $$2(\ ^{20}C_{5}\times \ ^{20}C_{6})$$
A team of $$11$$ students can be constituted in the following two ways$$i) 5$$ student from class $$XI$$ and $$6$$ from $$XII$$
$$ii) 6$$ student from class $$XI$$ and $$5$$ from $$XII$$
$$\therefore$$ The required number of ways
$$\Rightarrow \ ^{20}C_{5}\times \ ^{20}C_{6}+\ ^{20}C_{6}\times \ ^{20}C_{5}$$
$$\Rightarrow 2\left(\ ^{20}C_{5}\times \ ^{20}C_{6}\right)$$