The indian cricket team consists of 17 players.it includes 2 wicketkeepers 4 bowlers.in how many ways can a cricket eleven be selected if we have to select 1 wicketkeeper and atlest 3 bowlers.

Dear student
We are to choose 11 players including 1 wicket keeper and 3 bowlersor, 1 wicket keeper and 4 bowlers.Number of ways of selecting 1 wicket keeper, 3 bowlers and 7 other players=2C1.4C3.11C7=2×4!1! 3!×11!4! 7!=2×4×3!3!×11×10×9×8×7!4! 7!=8×330=2640Number of ways of selecting 1 wicket keeper, 4 bowlers and 6 other players=2C1.4C4.11C6=2×1×11!5! 6!=2×11×10×9×8×7×6!5×4×3×2×6!=924Theerfore, Total number of ways of selecting the team=2640+924=3564
Regards

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