Question

If a cricket team of $11$ players is to be selected from $8$ batsman, $6$ bowlers, $4$ all rounder and $2$ wicket keepers, then Number of selections when $2$ particular batsman dont 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 $2$ batsman dont want to play then the rest of $10$ players can be selected from $17$ other players
Number of selection $={{}^{17}}_{C_{10}}$
If the particular bowler doesn't play then number of selection ${{}^{19}}_{C_{11}}$
$\therefore$ Total number of selection $={{}^{17}}_{C_{10}}+{{}^{19}}_{C_{11}}$