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In how many ways can one select a cricket team of eleven from 13 players in which only 5 players can bowl. If each cricket team of 11 must include at least 4 bowlers.
- a)28
- b)40
- c)12
- d)68
Correct answer is option 'D'. Can you explain this answer?
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In how many ways can one select a cricket team of eleven from 13 playe...
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In how many ways can one select a cricket team of eleven from 13 playe...
Approach:
To solve this problem, we need to consider the different cases where the team can have 4, 5, 6, 7, or 8 bowlers. We will then calculate the number of ways to select the team for each case and add them up to get the total number of ways.
1. Case 1: Selecting 4 Bowlers
- Number of ways to select 4 bowlers from 5: 5C4 = 5
- Number of ways to select 7 players from the remaining 8: 8C7 = 8
- Total number of ways for this case: 5 * 8 = 40
2. Case 2: Selecting 5 Bowlers
- Number of ways to select 5 bowlers from 5: 5C5 = 1
- Number of ways to select 6 players from the remaining 8: 8C6 = 28
- Total number of ways for this case: 1 * 28 = 28
3. Case 3: Selecting 6, 7, or 8 Bowlers
- Since each team must include at least 4 bowlers, we cannot have a team with 6, 7, or 8 bowlers.
4. Total Number of Ways
- Total number of ways to select the cricket team = 40 (from Case 1) + 28 (from Case 2) = 68
Therefore, the correct answer is option D) 68.
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In how many ways can one select a cricket team of eleven from 13 players in which only 5 players can bowl. If each cricket team of 11 must include at least 4 bowlers.a)28b)40c)12d)68Correct answer is option 'D'. Can you explain this answer?
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