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A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is
- a)380
- b)320
- c)260
- d)95
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A debate club consists of 6 girls and 4 boys. A team of 4 members is t...
If a boy is selected then number of ways = 4C1.6C3
If a boy is not selcected then number of ways = 6C4
Captain can be selected in 4C1 ways
Required number of ways =
If a boy is not selcected then number of ways = 6C4
Captain can be selected in 4C1 ways
Required number of ways =
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A debate club consists of 6 girls and 4 boys. A team of 4 members is t...
To solve this problem, we need to consider the different scenarios for selecting the team. We have 6 girls and 4 boys, and we need to select a team of 4 members with at most one boy.
Let's break down the problem step by step:
Step 1: Selecting the captain
Since the captain can be selected from any of the 4 members, the number of ways to select the captain is 4C1 = 4.
Step 2: Selecting the remaining team members
Now, we need to select the remaining 3 members from the available 9 members (6 girls and 3 boys), with at most one boy.
Case 1: Selecting all girls
In this case, we need to select 3 girls from the 6 available. The number of ways to do this is 6C3 = 20.
Case 2: Selecting two girls and one boy
In this case, we need to select 2 girls from the 6 available and 1 boy from the 4 available. The number of ways to do this is 6C2 * 4C1 = 90.
Therefore, the total number of ways to select the remaining team members is 20 + 90 = 110.
Step 3: Multiply the number of ways for each step
To get the total number of ways to select the team, we multiply the number of ways for each step:
Total number of ways = Number of ways to select the captain * Number of ways to select the remaining team members
Total number of ways = 4 * 110 = 440.
However, we need to consider that the team can have at most one boy. So, we subtract the case where all girls are selected:
Total number of ways = 440 - 20 = 420.
Therefore, the correct answer is option A) 380.
Let's break down the problem step by step:
Step 1: Selecting the captain
Since the captain can be selected from any of the 4 members, the number of ways to select the captain is 4C1 = 4.
Step 2: Selecting the remaining team members
Now, we need to select the remaining 3 members from the available 9 members (6 girls and 3 boys), with at most one boy.
Case 1: Selecting all girls
In this case, we need to select 3 girls from the 6 available. The number of ways to do this is 6C3 = 20.
Case 2: Selecting two girls and one boy
In this case, we need to select 2 girls from the 6 available and 1 boy from the 4 available. The number of ways to do this is 6C2 * 4C1 = 90.
Therefore, the total number of ways to select the remaining team members is 20 + 90 = 110.
Step 3: Multiply the number of ways for each step
To get the total number of ways to select the team, we multiply the number of ways for each step:
Total number of ways = Number of ways to select the captain * Number of ways to select the remaining team members
Total number of ways = 4 * 110 = 440.
However, we need to consider that the team can have at most one boy. So, we subtract the case where all girls are selected:
Total number of ways = 440 - 20 = 420.
Therefore, the correct answer is option A) 380.
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A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club includingthe selection of a captain (from among these 4 members) for the team. If the team has to include at mostone boy, then the number of ways of selecting the team isa)380b)320c)260d)95Correct answer is option 'A'. Can you explain this answer?
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A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club includingthe selection of a captain (from among these 4 members) for the team. If the team has to include at mostone boy, then the number of ways of selecting the team isa)380b)320c)260d)95Correct answer is option 'A'. 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 A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club includingthe selection of a captain (from among these 4 members) for the team. If the team has to include at mostone boy, then the number of ways of selecting the team isa)380b)320c)260d)95Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club includingthe selection of a captain (from among these 4 members) for the team. If the team has to include at mostone boy, then the number of ways of selecting the team isa)380b)320c)260d)95Correct answer is option 'A'. Can you explain this answer?.
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