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You are selecting a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket keepers. In how many ways you can do it so that the team contains exactly 3 bowlers and 1 wicket keeper? Would your answer be different if the team contains at least 3 bowlers and at least 1 wicket-keeper?
- a)960
- b)2472
- c)840
- d)420
Correct answer is option 'A'. Can you explain this answer?
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You are selecting a cricket team of first 11 players out of 16 includi...
ANSWER :- A
Solution :-
There are : 4 bowlers, 2 wicket-keepers, 10 non-bowlers-not-wicket keepers.
There are exactly 3 bowlers, exactly 1 wicket keeper, and exactly 7 non-bowlers-non-wicket-keepers.
(4C3)(2C1)(10C7)
= 960
Most Upvoted Answer
You are selecting a cricket team of first 11 players out of 16 includi...
Solution:
We have to select a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket keepers.
We need to select exactly 3 bowlers and 1 wicket keeper.
Number of ways to select 3 bowlers from 4 bowlers = 4C3 = 4
Number of ways to select 1 wicket keeper from 2 wicket keepers = 2C1 = 2
Number of ways to select 7 remaining players from 10 players (16-3 bowlers-1 wicket keeper = 12, but we need to select 11, so 12-1) = 10C7 = 120
Total number of ways to select the team = 4 x 2 x 120 = 960
Therefore, the answer is option 'A' - 960.
If the team contains at least 3 bowlers and at least 1 wicket-keeper, the solution would be different. In that case, we need to find the total number of ways to select a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket keepers, where we can have 3 or 4 bowlers and 1 or 2 wicket keepers.
Total number of ways to select a team with at least 3 bowlers and 1 wicket-keeper:
Number of ways to select 3 bowlers and 1 wicket keeper = 4C3 x 2C1 = 8
Number of ways to select 2 bowlers and 2 wicket keepers = 4C2 x 2C2 = 6
Number of ways to select 4 bowlers and 1 wicket keeper = 4C4 x 2C1 = 2
Number of ways to select 3 bowlers and 2 wicket keepers = 4C3 x 2C2 = 4
Total number of ways = 8 + 6 + 2 + 4 = 20
Number of ways to select remaining 6 players from 10 players (16-3 bowlers-1 wicket keeper = 12, but we need to select 6, so 12-6) = 10C6 = 210
Total number of ways to select the team = 20 x 210 = 4200
Therefore, the answer is option 'D' - 4200.
We have to select a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket keepers.
We need to select exactly 3 bowlers and 1 wicket keeper.
Number of ways to select 3 bowlers from 4 bowlers = 4C3 = 4
Number of ways to select 1 wicket keeper from 2 wicket keepers = 2C1 = 2
Number of ways to select 7 remaining players from 10 players (16-3 bowlers-1 wicket keeper = 12, but we need to select 11, so 12-1) = 10C7 = 120
Total number of ways to select the team = 4 x 2 x 120 = 960
Therefore, the answer is option 'A' - 960.
If the team contains at least 3 bowlers and at least 1 wicket-keeper, the solution would be different. In that case, we need to find the total number of ways to select a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket keepers, where we can have 3 or 4 bowlers and 1 or 2 wicket keepers.
Total number of ways to select a team with at least 3 bowlers and 1 wicket-keeper:
Number of ways to select 3 bowlers and 1 wicket keeper = 4C3 x 2C1 = 8
Number of ways to select 2 bowlers and 2 wicket keepers = 4C2 x 2C2 = 6
Number of ways to select 4 bowlers and 1 wicket keeper = 4C4 x 2C1 = 2
Number of ways to select 3 bowlers and 2 wicket keepers = 4C3 x 2C2 = 4
Total number of ways = 8 + 6 + 2 + 4 = 20
Number of ways to select remaining 6 players from 10 players (16-3 bowlers-1 wicket keeper = 12, but we need to select 6, so 12-6) = 10C6 = 210
Total number of ways to select the team = 20 x 210 = 4200
Therefore, the answer is option 'D' - 4200.
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You are selecting a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket keepers. In how many ways you can do it so that the team contains exactly 3 bowlers and 1 wicket keeper? Would your answer be different if the team contains at least 3 bowlers and at least 1 wicket-keeper?a)960b)2472c)840d)420Correct answer is option 'A'. Can you explain this answer?
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