Question

A cricket club has $15$ members of whom $5$$arebowlersandtherestarebatsmen.Inhowmanywayscan$10$playersbechosensoastoinclude$3$ bowlers?

• A. $200$
• B. $1200$
• C. $320$
• D. $50$

Answer 1

The correct option is B $1200$

$15$ members
$5$ bowlers
$10$ batsmen
$3$ bowlers can be chosen in ${}^5{C}_3$ ways and the remaining 7 batsmen can be chosen in
${}^{10}{C}_7$ ways.
Therefore,
${}^5{C}_3{+}^{10}{C}_7=\frac{5!}{2!\times 3!}\times \frac{10!}{3!7!}$
$=\frac{5\times 4}{2}\times \frac{10\times 9\times 8}{3\times 2}$
$=10\times 120=1200$