In how many ways 11 players can be selected from 15 players, if only 6 of these players can bowl and the 11 players must include atleast 4 bowlers?
Text Solution
Verified by Experts1170
(1170)
Sol. Total No. of bowlers = 6
Now, (i) If 4 bowlers are including the no. of ways
selecting 11 players out of 15 players = 6 C 4 × 9 C 7 = 15 × 36 = 540
(ii) If 5 bowlers are selected = 6 C 5 × 9 C 6 = 6 × 84 = 504
(iii) If all 6 bowlers are selected = 6 C 6 × 9 C 5 = 1 × 126 = 126
Hence total no. of ways = 540 + 504 + 126 = 1170
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