First slide

Combinations

Question

In a group of 13 cricket players, 4 are bowlers. Then in how many ways can they form a cricket team of 11 players in which at least 2 bowlers are included?

Moderate

A

55
B

72
C

78
D

none of these

Solution

The number of ways can be given as follows:
2 bowlers and 9 other players: $^{4} C_{2} \times^{9} C_{9}$
3 bowlers and 8 other players $^{4} C_{3} \times^{9} C_{8}$
4 bowlers and 7 other players: $^{4} C_{4} \times^{9} C_{7}$
Hence, required number of ways is $6 \times 1 + 4 \times 9 + 1 \times 36 = 78$ .

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