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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 fomied from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:
- a)200
- b)300
- c)500
- d)350
Correct answer is option 'B'. Can you explain this answer?
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Consider a class of 5 girls and 7 boys. The number of different teams ...
Required number of ways
= Total number of ways – When A and B are always included.
= 5C2 . 7C3 - 5C1 . 5C2 = 300
= Total 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 ...
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Consider a class of 5 girls and 7 boys. The number of different teams ...
Problem:
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 members of the same team, is:
a) 200
b) 300
c) 500
d) 350
Explanation:
To solve this problem, we can use the concept of combinations.
Total number of teams:
First, let's calculate the total number of teams we can form.
- We need to select 2 girls out of 5, which can be done in 5C2 ways (read as "5 choose 2").
- We also need to select 3 boys out of 7, which can be done in 7C3 ways.
- Hence, the total number of teams we can form is (5C2) * (7C3).
Teams with A and B together:
Now, let's calculate the number of teams in which boys A and B are together.
- We can treat A and B as a single entity, and select 2 girls out of 5, which can be done in 5C2 ways.
- We also need to select 1 more boy out of the remaining 5 boys (excluding A and B), which can be done in 5C1 ways.
- Hence, the number of teams in which A and B are together is (5C2) * (5C1).
Teams with A and B apart:
Finally, let's calculate the number of teams in which boys A and B are apart.
- We can subtract the number of teams in which A and B are together from the total number of teams.
- So, the number of teams in which A and B are apart is (5C2) * (7C3) - (5C2) * (5C1).
Calculating the final answer:
Now, we can substitute the values into the above expression and calculate the final answer.
- (5C2) = 5! / (2! * (5-2)!) = 10
- (7C3) = 7! / (3! * (7-3)!) = 35
- (5C1) = 5! / (1! * (5-1)!) = 5
So, the number of teams in which boys A and B are apart is (10 * 35) - (10 * 5) = 350.
Hence, the correct answer is option b) 300.
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 members of the same team, is:
a) 200
b) 300
c) 500
d) 350
Explanation:
To solve this problem, we can use the concept of combinations.
Total number of teams:
First, let's calculate the total number of teams we can form.
- We need to select 2 girls out of 5, which can be done in 5C2 ways (read as "5 choose 2").
- We also need to select 3 boys out of 7, which can be done in 7C3 ways.
- Hence, the total number of teams we can form is (5C2) * (7C3).
Teams with A and B together:
Now, let's calculate the number of teams in which boys A and B are together.
- We can treat A and B as a single entity, and select 2 girls out of 5, which can be done in 5C2 ways.
- We also need to select 1 more boy out of the remaining 5 boys (excluding A and B), which can be done in 5C1 ways.
- Hence, the number of teams in which A and B are together is (5C2) * (5C1).
Teams with A and B apart:
Finally, let's calculate the number of teams in which boys A and B are apart.
- We can subtract the number of teams in which A and B are together from the total number of teams.
- So, the number of teams in which A and B are apart is (5C2) * (7C3) - (5C2) * (5C1).
Calculating the final answer:
Now, we can substitute the values into the above expression and calculate the final answer.
- (5C2) = 5! / (2! * (5-2)!) = 10
- (7C3) = 7! / (3! * (7-3)!) = 35
- (5C1) = 5! / (1! * (5-1)!) = 5
So, the number of teams in which boys A and B are apart is (10 * 35) - (10 * 5) = 350.
Hence, the correct answer is option b) 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 fomied from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:a)200b)300c)500d)350Correct answer is option 'B'. 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 fomied from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:a)200b)300c)500d)350Correct answer is option 'B'. 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 fomied from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:a)200b)300c)500d)350Correct answer is option 'B'. 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 fomied from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:a)200b)300c)500d)350Correct answer is option 'B'. Can you explain this answer?.
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