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Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:
Correct answer is '300'. Can you explain this answer?
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Most Upvoted Answer
Consider a class of 5 girls and 7 boys. The number of different teams...
Given:
- Number of girls = 5
- Number of boys = 7
- We need to form teams of 2 girls and 3 boys
Approach:
To solve this problem, we can use the concept of combinations.
Step 1: Selecting 2 girls
- We need to select 2 girls from the class of 5.
- The number of ways to select 2 girls out of 5 can be calculated using the combination formula: C(5, 2) = 5! / (2! * (5-2)!) = 10.
Step 2: Selecting 3 boys
- We need to select 3 boys from the class of 7, excluding boys A and B who refuse to be in the same team.
- The number of ways to select 3 boys out of 7 can be calculated using the combination formula: C(7, 3) = 7! / (3! * (7-3)!) = 35.
Step 3: Calculating the total number of teams
- Once we have selected 2 girls and 3 boys, we can form a team.
- The total number of teams can be calculated by multiplying the number of ways to select girls and boys: 10 * 35 = 350.
Step 4: Removing the invalid teams
- Now, we need to remove the teams where boys A and B are in the same team.
- For each valid team, there are 2 possible cases: A is selected and B is not, or A is not selected and B is.
- Number of valid teams = total teams - invalid teams = 350 - 2 = 348.
Final Answer:
The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, considering boys A and B, who refuse to be in the same team, is 348.
- Number of girls = 5
- Number of boys = 7
- We need to form teams of 2 girls and 3 boys
Approach:
To solve this problem, we can use the concept of combinations.
Step 1: Selecting 2 girls
- We need to select 2 girls from the class of 5.
- The number of ways to select 2 girls out of 5 can be calculated using the combination formula: C(5, 2) = 5! / (2! * (5-2)!) = 10.
Step 2: Selecting 3 boys
- We need to select 3 boys from the class of 7, excluding boys A and B who refuse to be in the same team.
- The number of ways to select 3 boys out of 7 can be calculated using the combination formula: C(7, 3) = 7! / (3! * (7-3)!) = 35.
Step 3: Calculating the total number of teams
- Once we have selected 2 girls and 3 boys, we can form a team.
- The total number of teams can be calculated by multiplying the number of ways to select girls and boys: 10 * 35 = 350.
Step 4: Removing the invalid teams
- Now, we need to remove the teams where boys A and B are in the same team.
- For each valid team, there are 2 possible cases: A is selected and B is not, or A is not selected and B is.
- Number of valid teams = total teams - invalid teams = 350 - 2 = 348.
Final Answer:
The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, considering boys A and B, who refuse to be in the same team, is 348.
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Community Answer
Consider a class of 5 girls and 7 boys. The number of different teams...
Given: Total number of girls = 5 and total number of boys = 7
Team members: number of girls = 2 and number of boys = 3
Total number of ways = 5C2 . 7C3
Consider when A and B are always included = 5C1 5C2 as only 1 boy and 2 girls are to be selected.
Required number of ways = Total number of ways - number of ways when A and B are always included
= 5C2 7C3 - 5C1 5C2 = 300
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Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:Correct answer is '300'. Can you explain this answer?
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Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:Correct answer is '300'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:Correct answer is '300'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:Correct answer is '300'. Can you explain this answer?.
Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:Correct answer is '300'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:Correct answer is '300'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:Correct answer is '300'. Can you explain this answer?.
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