<s>[INST] Combination questions Q: A team of $11$ is to be chosen out of $15$ cricketers of whom $5$ are bowlers and $2$ others are wicket keepers. In how many ways can this be done so that the team contains at least $4$ bowlers and at least $1$ wicket keeper?
 [/INST] $$\binom{5}{4}\binom{2}{1}\binom{8}{6}+\binom{5}{5}\binom{2}{1}\binom{8}{5}+\binom{5}{4}\binom{2}{2}\binom{8}{5}+\binom{5}{5}\binom{2}{2}\binom{8}{4}$$
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