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In a group of...

Question

In a group of 6 batsmen and 4 bowlers, four cricketers are to be selected. In how many different ways can they be selected such that at least one batsman should be there?

159

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194

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205

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209

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Solution

The correct option is D 209
We may have (1 batsman and 3 bowlers) or (2 batsmen and 2 bowlers) or (3 batsmen and 1 bowler) or (4 batsmen).
Therefore, Required number of ways $= (^{6} C_{4} \times^{4} C_{3}) + (^{6} C_{2} \times^{4} C_{2}) + (^{6} C_{3} \times^{4} C_{1}) +^{6} C_{4} = (^{6} C_{1} \times^{4} C_{1}) + (^{6} C_{2} \times^{4} C_{2}) + (^{6} C_{3} \times^{4} C_{1}) +^{6} C_{2} = 24 + 90 + 80 + 15 = 209$

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In a group of 6 batsmen and 4 bowlers, four cricketers are to be selected. In how many different ways can they be selected such that at least one batsman should be there?

The correct option is D 209We may have (1 batsman and 3 bowlers) or (2 batsmen and 2 bowlers) or (3 batsmen and 1 bowler) or (4 batsmen). Therefore, Required number of ways =(6C4×4C3)+(6C2×4C2)+(6C3×4C1)+6C4=(6C1×4C1)+(6C2×4C2)+(6C3×4C1)+6C2=24+90+80+15=209