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A cricket team of eleven players is to be selected out 6 batsmen, 5 bowlers, 2 all-rounders and 3 wicket keepers. Consider an all-rounder as a player who is a batsman as well as a blower.

The number selection containing exactly one wicket and at least one all-rounder is:

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C_{1}^{2} (2 C_{9}^{11} + C_{8}^{11})

C_{1}^{2} \times C_{9}^{2} \times C_{9}^{11}

C_{1}^{2} (C_{3}^{12} + C_{3}^{11})

C_{1}^{4} \times C_{9}^{11}

answer is A.

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Detailed Solution

In a cricket team total players =11
In a cricket team total batsman =6
In a cricket team total bowlers =5
In a cricket team total all rounder =2
In a cricket team total wicket keepers =2
Case 1:
When one all-rounder and one wicket keeper,

C_{1}^{2} \times C_{1}^{2} \times C_{9}^{11}

Case 2:
When two all- rounder and one wicket keeper

C_{2}^{2} \times C_{1}^{2} \times C_{8}^{11}

Total ways =

C_{1}^{2} \times C_{1}^{2} \times C_{9}^{11}

C_{2}^{2} \times C_{1}^{2} \times C_{8}^{11}

C_{1}^{2} \times (C_{1}^{2} \times C_{9}^{11} + C_{2}^{2} \times C_{8}^{11}) = C_{1}^{2} \times (2 C_{9}^{11} + C_{8}^{11})

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