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 a particular batsman and a particular wicket keeper do not want to play together, is

• A. $2^{18}{C}_{10}$
• B. ${}^{19}{C}_{11}{+}^{18}{C}_{10}$
• C. ${}^{19}{C}_{10}{+}^{19}{C}_{11}$
• D. None of these

Answer 1

The correct option is B ${}^{19}{C}_{11}{+}^{18}{C}_{10}$

If the particular batsman is selected, then rest of $10$ players can be selected in ${}^{18}{C}_{10}$ ways.

If particular wicketkeeper is selected, then rest of $10$ players can be selected in ${}^{18}{C}_{10}$ ways.

If both are not selected, then number of ways is ${}^{18}{C}_{11}$.

Hence, total number of ways is $2{\cdot }^{18}{C}_{10}+{}^{18}{C}_{11}={}^{19}{C}_{11}+{}^{18}{C}_{10}$.