The Indian Cricket team consists of 16 players. It includes 1 wicket keeper and 7 bowlers. In how ma

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16 Dec 2016 Combination

The Indian Cricket team consists of 16 players. It includes 1 wicket keeper and 7 bowlers. In how many ways can a playing eleven be selected if we have to select 1 wicket keeper and at least 5 bowlers?

OPtion

1) 496
2) 784
3) 932
4) 1176
5) 1284
6) 1336
7) 1492
8) 1582
9) 1666
10)1722

Solution

We have to choose 11 players including:
- 1 wicket keeper and 5 bowlers or
- 1 wicket keeper and 6 bowlers or
- 1 wicket keeper and 7 bowlers.
Number of ways of selecting 1 wicket keeper, 5 bowlers and 5 other players
=1C1*7C5*8C5= 1*21*56 = 1176
Number of ways of selecting 1 wicket keeper, 6 bowlers and 4 other players
=1C1*7C6*8C4= 1*7*70 = 490
Number of ways of selecting 1 wicket keeper, 7 bowlers and 3 other players
=1C1*7C7*8C3=1*1*56 = 56
=> Total number of ways of selecting the team:
=1176+490+56= 1722

Option 10)

Correct Option: 10 Best Solution (0)