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In how many ways a team of 7 players out of 6 boys and 5 girls can be made such that at most 3 girls are there in the team?
- a)215
- b)218
- c)220
- d)214
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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In how many ways a team of 7 players out of 6 boys and 5 girls can be ...
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In how many ways a team of 7 players out of 6 boys and 5 girls can be ...
Approach:
To find the number of ways a team of 7 players can be formed with at most 3 girls, we will consider the following cases:
1. 0 girls and 7 boys in the team
2. 1 girl and 6 boys in the team
3. 2 girls and 5 boys in the team
4. 3 girls and 4 boys in the team
Solution:
Case 1: 0 girls and 7 boys
Number of ways to select 7 boys out of 6 boys = 6C7 = 6 ways
Case 2: 1 girl and 6 boys
Number of ways to select 1 girl out of 5 girls = 5C1 = 5 ways
Number of ways to select 6 boys out of 6 boys = 6C6 = 1 way
Total number of ways = 5 * 1 = 5 ways
Case 3: 2 girls and 5 boys
Number of ways to select 2 girls out of 5 girls = 5C2 = 10 ways
Number of ways to select 5 boys out of 6 boys = 6C5 = 6 ways
Total number of ways = 10 * 6 = 60 ways
Case 4: 3 girls and 4 boys
Number of ways to select 3 girls out of 5 girls = 5C3 = 10 ways
Number of ways to select 4 boys out of 6 boys = 6C4 = 15 ways
Total number of ways = 10 * 15 = 150 ways
Total number of ways:
Adding all the cases, the total number of ways = 6 + 5 + 60 + 150 = 215 ways
Therefore, the correct answer is option A) 215.
To find the number of ways a team of 7 players can be formed with at most 3 girls, we will consider the following cases:
1. 0 girls and 7 boys in the team
2. 1 girl and 6 boys in the team
3. 2 girls and 5 boys in the team
4. 3 girls and 4 boys in the team
Solution:
Case 1: 0 girls and 7 boys
Number of ways to select 7 boys out of 6 boys = 6C7 = 6 ways
Case 2: 1 girl and 6 boys
Number of ways to select 1 girl out of 5 girls = 5C1 = 5 ways
Number of ways to select 6 boys out of 6 boys = 6C6 = 1 way
Total number of ways = 5 * 1 = 5 ways
Case 3: 2 girls and 5 boys
Number of ways to select 2 girls out of 5 girls = 5C2 = 10 ways
Number of ways to select 5 boys out of 6 boys = 6C5 = 6 ways
Total number of ways = 10 * 6 = 60 ways
Case 4: 3 girls and 4 boys
Number of ways to select 3 girls out of 5 girls = 5C3 = 10 ways
Number of ways to select 4 boys out of 6 boys = 6C4 = 15 ways
Total number of ways = 10 * 15 = 150 ways
Total number of ways:
Adding all the cases, the total number of ways = 6 + 5 + 60 + 150 = 215 ways
Therefore, the correct answer is option A) 215.
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In how many ways a team of 7 players out of 6 boys and 5 girls can be made such that at most 3 girls are there in the team?a)215b)218c)220d)214e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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