Question

We have to choose $11$ players for cricket team from eight batsmen, six bowlers, four all-rounders and two wicket-keepers. The number of selections when only one all-rounder and one wicket-keeper will play, is

• A. $8\times {}^{14}{C}_9$
• B. $8\times {}^{18}{C}_9$
• C. ${}^{18}{C}_{11}$
• D. None of these

Answer 1

The correct option is A $8\times {}^{14}{C}_9$

Number of ways in which one all-rounder and one wicket-keeper can be selected $=2\times 4=8$

So only $9$ players need to be selected from $14$ players and that can be done in ${}^{14}{C}_9$

So total number possible teams can be made $=8\times {}^{14}{C}_9$