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A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together is
- a)164
- b)140
- c)112
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A lady arranges a dinner party for 6 guests .The number of ways in whi...
Case I : Both of them don't attend the party.then, no of ways = 8C6 = 28Case
II : Either of them is selected for party.then, no of ways = 2C1 * 8C5 = 112
Total no of ways = 112+28 = 140
Most Upvoted Answer
A lady arranges a dinner party for 6 guests .The number of ways in whi...
Given:
Number of guests = 6
Number of friends = 10
2 friends cannot attend the party together
To find:
Number of ways to select 6 guests
Solution:
We can solve this problem using the principle of inclusion-exclusion.
Let A be the event that the two friends who cannot attend the party are selected together.
Let B be the event that the two friends who cannot attend the party are not selected together.
Total number of ways to select 6 guests from 10 friends = 10C6 = 210
We want to find the number of ways in which B can occur, i.e., the number of ways to select 6 guests such that the two friends who cannot attend the party are not selected together.
Number of ways in which A can occur:
We can first select the two friends who cannot attend the party together in 8C2 ways. We then have to select 4 guests from the remaining 8 friends, which can be done in 8C4 ways. Therefore, the number of ways in which A can occur = 8C2 * 8C4 = 420.
Number of ways in which neither A nor B can occur:
This means that both the friends who cannot attend the party must be selected. We can select them in 2C2 ways. We then have to select 4 guests from the remaining 8 friends, which can be done in 8C4 ways. Therefore, the number of ways in which neither A nor B can occur = 2C2 * 8C4 = 70.
Using the principle of inclusion-exclusion, we can find the number of ways in which B can occur:
Number of ways in which B can occur = Total number of ways - Number of ways in which A can occur + Number of ways in which neither A nor B can occur
= 210 - 420 + 70
= - 140 (which is not possible)
Therefore, the number of ways in which B can occur = 210 - 420 + 70 = 140.
Hence, the correct option is (b) 140.
Number of guests = 6
Number of friends = 10
2 friends cannot attend the party together
To find:
Number of ways to select 6 guests
Solution:
We can solve this problem using the principle of inclusion-exclusion.
Let A be the event that the two friends who cannot attend the party are selected together.
Let B be the event that the two friends who cannot attend the party are not selected together.
Total number of ways to select 6 guests from 10 friends = 10C6 = 210
We want to find the number of ways in which B can occur, i.e., the number of ways to select 6 guests such that the two friends who cannot attend the party are not selected together.
Number of ways in which A can occur:
We can first select the two friends who cannot attend the party together in 8C2 ways. We then have to select 4 guests from the remaining 8 friends, which can be done in 8C4 ways. Therefore, the number of ways in which A can occur = 8C2 * 8C4 = 420.
Number of ways in which neither A nor B can occur:
This means that both the friends who cannot attend the party must be selected. We can select them in 2C2 ways. We then have to select 4 guests from the remaining 8 friends, which can be done in 8C4 ways. Therefore, the number of ways in which neither A nor B can occur = 2C2 * 8C4 = 70.
Using the principle of inclusion-exclusion, we can find the number of ways in which B can occur:
Number of ways in which B can occur = Total number of ways - Number of ways in which A can occur + Number of ways in which neither A nor B can occur
= 210 - 420 + 70
= - 140 (which is not possible)
Therefore, the number of ways in which B can occur = 210 - 420 + 70 = 140.
Hence, the correct option is (b) 140.
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A lady arranges a dinner party for 6 guests .The number of ways in whi...
Option B
140
140
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A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together isa)164b)140c)112d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together isa)164b)140c)112d)none of theseCorrect 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 lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together isa)164b)140c)112d)none of theseCorrect 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 lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together isa)164b)140c)112d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together isa)164b)140c)112d)none of theseCorrect 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 lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together isa)164b)140c)112d)none of theseCorrect 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 lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together isa)164b)140c)112d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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