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A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :
- a)484
- b)485
- c)468
- d)469
Correct answer is option 'B'. Can you explain this answer?
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To solve this problem, we can break it down into different cases based on the number of ladies and men each person invites to the party.
Case 1: X invites 2 ladies and 1 man, Y invites 1 lady and 2 men.
In this case, X can choose 2 ladies from his 4 lady friends in 4C2 ways, and 1 man from his 3 male friends in 3C1 ways. Similarly, Y can choose 1 lady from her 3 lady friends in 3C1 ways, and 2 men from her 4 male friends in 4C2 ways. Therefore, the total number of ways for this case is 4C2 * 3C1 * 3C1 * 4C2 = 6 * 3 * 3 * 6 = 324.
Case 2: X invites 1 lady and 2 men, Y invites 2 ladies and 1 man.
In this case, X can choose 1 lady from his 4 lady friends in 4C1 ways, and 2 men from his 3 male friends in 3C2 ways. Similarly, Y can choose 2 ladies from her 3 lady friends in 3C2 ways, and 1 man from her 4 male friends in 4C1 ways. Therefore, the total number of ways for this case is 4C1 * 3C2 * 3C2 * 4C1 = 4 * 3 * 3 * 4 = 144.
Case 3: X invites 3 ladies and 0 men, Y invites 0 ladies and 3 men.
In this case, X can choose 3 ladies from his 4 lady friends in 4C3 ways. Similarly, Y can choose 3 men from her 4 male friends in 4C3 ways. Therefore, the total number of ways for this case is 4C3 * 4C3 = 4 * 4 = 16.
Adding up the total number of ways from each case, we get 324 + 144 + 16 = 484.
Therefore, the correct answer is option B) 485.
Note: The question states that 3 friends of each X and Y must be in the party, so we do not need to consider cases where X or Y invite fewer than 3 friends.
Case 1: X invites 2 ladies and 1 man, Y invites 1 lady and 2 men.
In this case, X can choose 2 ladies from his 4 lady friends in 4C2 ways, and 1 man from his 3 male friends in 3C1 ways. Similarly, Y can choose 1 lady from her 3 lady friends in 3C1 ways, and 2 men from her 4 male friends in 4C2 ways. Therefore, the total number of ways for this case is 4C2 * 3C1 * 3C1 * 4C2 = 6 * 3 * 3 * 6 = 324.
Case 2: X invites 1 lady and 2 men, Y invites 2 ladies and 1 man.
In this case, X can choose 1 lady from his 4 lady friends in 4C1 ways, and 2 men from his 3 male friends in 3C2 ways. Similarly, Y can choose 2 ladies from her 3 lady friends in 3C2 ways, and 1 man from her 4 male friends in 4C1 ways. Therefore, the total number of ways for this case is 4C1 * 3C2 * 3C2 * 4C1 = 4 * 3 * 3 * 4 = 144.
Case 3: X invites 3 ladies and 0 men, Y invites 0 ladies and 3 men.
In this case, X can choose 3 ladies from his 4 lady friends in 4C3 ways. Similarly, Y can choose 3 men from her 4 male friends in 4C3 ways. Therefore, the total number of ways for this case is 4C3 * 4C3 = 4 * 4 = 16.
Adding up the total number of ways from each case, we get 324 + 144 + 16 = 484.
Therefore, the correct answer is option B) 485.
Note: The question states that 3 friends of each X and Y must be in the party, so we do not need to consider cases where X or Y invite fewer than 3 friends.
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A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :a)484b)485c)468d)469Correct answer is option 'B'. Can you explain this answer?
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A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :a)484b)485c)468d)469Correct 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 A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :a)484b)485c)468d)469Correct 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 A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :a)484b)485c)468d)469Correct answer is option 'B'. Can you explain this answer?.
A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :a)484b)485c)468d)469Correct 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 A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :a)484b)485c)468d)469Correct 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 A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :a)484b)485c)468d)469Correct answer is option 'B'. Can you explain this answer?.
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