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There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicket keeper, is _________.
Correct answer is '777'. Can you explain this answer?
Most Upvoted Answer
There are 15 players in a cricket team, out of which 6 are bowlers, 7 ...
Given:
- Total number of players in the team = 15
- Number of bowlers = 6
- Number of batsmen = 7
- Number of wicket keepers = 2
To find: The number of ways to select a team of 11 players that includes at least 4 bowlers, 5 batsmen, and 1 wicket keeper.
Approach:
To find the number of ways to select a team, we will consider the different scenarios based on the number of bowlers selected.
Case 1: Selecting 4 bowlers
- We need to select 4 bowlers from the given 6 bowlers.
- The remaining 7 players need to be selected from the batsmen and wicket keepers.
- Number of ways to select 4 bowlers = C(6, 4)
- Number of ways to select the remaining 7 players = C(7, 7) + C(7, 6) + C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)
- Total number of ways = C(6, 4) * [C(7, 7) + C(7, 6) + C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)]
Case 2: Selecting 5 bowlers
- We need to select 5 bowlers from the given 6 bowlers.
- The remaining 6 players need to be selected from the batsmen and wicket keepers.
- Number of ways to select 5 bowlers = C(6, 5)
- Number of ways to select the remaining 6 players = C(7, 6) + C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)
- Total number of ways = C(6, 5) * [C(7, 6) + C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)]
Case 3: Selecting 6 bowlers
- We need to select all 6 bowlers from the given 6 bowlers.
- The remaining 5 players need to be selected from the batsmen and wicket keepers.
- Number of ways to select 6 bowlers = C(6, 6)
- Number of ways to select the remaining 5 players = C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)
- Total number of ways = C(6, 6) * [C(7, 5
- Total number of players in the team = 15
- Number of bowlers = 6
- Number of batsmen = 7
- Number of wicket keepers = 2
To find: The number of ways to select a team of 11 players that includes at least 4 bowlers, 5 batsmen, and 1 wicket keeper.
Approach:
To find the number of ways to select a team, we will consider the different scenarios based on the number of bowlers selected.
Case 1: Selecting 4 bowlers
- We need to select 4 bowlers from the given 6 bowlers.
- The remaining 7 players need to be selected from the batsmen and wicket keepers.
- Number of ways to select 4 bowlers = C(6, 4)
- Number of ways to select the remaining 7 players = C(7, 7) + C(7, 6) + C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)
- Total number of ways = C(6, 4) * [C(7, 7) + C(7, 6) + C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)]
Case 2: Selecting 5 bowlers
- We need to select 5 bowlers from the given 6 bowlers.
- The remaining 6 players need to be selected from the batsmen and wicket keepers.
- Number of ways to select 5 bowlers = C(6, 5)
- Number of ways to select the remaining 6 players = C(7, 6) + C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)
- Total number of ways = C(6, 5) * [C(7, 6) + C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)]
Case 3: Selecting 6 bowlers
- We need to select all 6 bowlers from the given 6 bowlers.
- The remaining 5 players need to be selected from the batsmen and wicket keepers.
- Number of ways to select 6 bowlers = C(6, 6)
- Number of ways to select the remaining 5 players = C(7, 5) + C(7, 4) + C(7, 3) + C(7, 2) + C(7, 1) + C(7, 0)
- Total number of ways = C(6, 6) * [C(7, 5
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Community Answer
There are 15 players in a cricket team, out of which 6 are bowlers, 7 ...
15: Players
6: Bowlers
7: Batsmen
2: Wicket keepers
Total number of ways for:
at least 4 blowers, 5 batsmen and 1 wicket keeper
6: Bowlers
7: Batsmen
2: Wicket keepers
Total number of ways for:
at least 4 blowers, 5 batsmen and 1 wicket keeper
= 777
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There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicket keeper, is _________.Correct answer is '777'. Can you explain this answer?
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There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicket keeper, is _________.Correct answer is '777'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicket keeper, is _________.Correct answer is '777'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicket keepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicket keeper, is _________.Correct answer is '777'. Can you explain this answer?.
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