Question

We have to choose $11$ players for cricket team from $8$ batsmen, $6$ bowlers, $4$ all rounders and $2$ wicket keepers. Number of selections, when two particular batsmen do not want to play when a particular bowler will play, is

• A. ${}^{17}{C}_{10}+{}^{19}{C}_{11}$
• B. ${}^{17}{C}_{10}+{}^{19}{C}_{11}+{}^{17}{C}_{11}$
• C. ${}^{17}{C}_{10}+{}^{20}{C}_{11}$
• D. ${}^{19}{C}_{10}+{}^{19}{C}_{11}$

Answer 1

The correct option is A ${}^{17}{C}_{10}+{}^{19}{C}_{11}$

If the particular bowler plays then two batsmen will not play. So, rest of $10$ players can be selected from $17$ other players. Number of such selections is ${}^{17}{C}_{10}$.

If the particular bowler does not play, then number of selections is ${}^{19}{C}_{11}$.

Hence total number of selections is $={}^{17}{C}_{10}+{}^{19}{C}_{11}$.