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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:
Correct answer is '485'. 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...
Given information:
- Man 'x' has 7 friends: 4 ladies and 3 men.
- His wife 'y' has 7 friends: 3 ladies and 4 men.
- 'x' and 'y' have no common friends.
- We need to find the total number of ways in which 'x' and 'y' together can throw a party inviting 3 ladies and 3 men, with 3 friends of each of 'x' and 'y' in this party.
Solution:
To solve this problem, we can consider the following steps:
Step 1: Select 3 ladies from 'x's friends:
- Since 'x' has 4 lady friends, we need to select 3 out of them.
- This can be done in 4C3 ways, which is equal to 4.
Step 2: Select 3 men from 'x's friends:
- Since 'x' has 3 male friends, we need to select 3 out of them.
- This can be done in 3C3 ways, which is equal to 1.
Step 3: Select 0 ladies from 'y's friends:
- Since 'y' has 3 lady friends, we need to select 0 out of them.
- This can be done in 3C0 ways, which is equal to 1.
Step 4: Select 3 men from 'y's friends:
- Since 'y' has 4 male friends, we need to select 3 out of them.
- This can be done in 4C3 ways, which is equal to 4.
Step 5: Arrange the selected friends:
- Now, we need to arrange the selected friends in the party.
- The 3 selected ladies from 'x' can be arranged among themselves in 3! ways, which is equal to 6.
- The 3 selected men from 'x' can be arranged among themselves in 3! ways, which is equal to 6.
- The 3 selected men from 'y' can be arranged among themselves in 3! ways, which is equal to 6.
Step 6: Calculate the total number of ways:
- To calculate the total number of ways, we need to multiply the number of ways from each step.
- Total number of ways = (4C3) * (3C3) * (3C0) * (4C3) * 3! * 3! * 3!
- Simplifying the expression, we get: 4 * 1 * 1 * 4 * 6 * 6 * 6 = 3456.
Therefore, 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 3456.
- Man 'x' has 7 friends: 4 ladies and 3 men.
- His wife 'y' has 7 friends: 3 ladies and 4 men.
- 'x' and 'y' have no common friends.
- We need to find the total number of ways in which 'x' and 'y' together can throw a party inviting 3 ladies and 3 men, with 3 friends of each of 'x' and 'y' in this party.
Solution:
To solve this problem, we can consider the following steps:
Step 1: Select 3 ladies from 'x's friends:
- Since 'x' has 4 lady friends, we need to select 3 out of them.
- This can be done in 4C3 ways, which is equal to 4.
Step 2: Select 3 men from 'x's friends:
- Since 'x' has 3 male friends, we need to select 3 out of them.
- This can be done in 3C3 ways, which is equal to 1.
Step 3: Select 0 ladies from 'y's friends:
- Since 'y' has 3 lady friends, we need to select 0 out of them.
- This can be done in 3C0 ways, which is equal to 1.
Step 4: Select 3 men from 'y's friends:
- Since 'y' has 4 male friends, we need to select 3 out of them.
- This can be done in 4C3 ways, which is equal to 4.
Step 5: Arrange the selected friends:
- Now, we need to arrange the selected friends in the party.
- The 3 selected ladies from 'x' can be arranged among themselves in 3! ways, which is equal to 6.
- The 3 selected men from 'x' can be arranged among themselves in 3! ways, which is equal to 6.
- The 3 selected men from 'y' can be arranged among themselves in 3! ways, which is equal to 6.
Step 6: Calculate the total number of ways:
- To calculate the total number of ways, we need to multiply the number of ways from each step.
- Total number of ways = (4C3) * (3C3) * (3C0) * (4C3) * 3! * 3! * 3!
- Simplifying the expression, we get: 4 * 1 * 1 * 4 * 6 * 6 * 6 = 3456.
Therefore, 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 3456.
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Community Answer
A man 'x' has 7 friends, 4 of them are ladies and 3 are men. His wife...
Required number of ways = 4C0.3C3.3C3.4C0 + 4C1.3C2.3C2.4C1 + 4C2.3C1.3C1.4C2 + 4C3.3C0.4C3
= 485
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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:Correct answer is '485'. 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:Correct answer is '485'. 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:Correct answer is '485'. 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:Correct answer is '485'. 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:Correct answer is '485'. 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:Correct answer is '485'. 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:Correct answer is '485'. Can you explain this answer?.
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