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A lady gives a dinner party to 6 guests . The no.of ways in which they may be selected from among 10 friends ,if two of the friends will not attend the party together?
Most Upvoted Answer
A lady gives a dinner party to 6 guests . The no.of ways in which they...
Total number of friends=10,
no. of friends to be selected=6,
required number of ways= total number of ways - total number of ways of selecting two friends always,
ways of selecting 6 friends among 10=10C6,
=10!/6!4!=210ways,
total number of selecting two friends always=
2C2×8C4=8!/4!4!=70,
required number of ways=210-70=140
no. of friends to be selected=6,
required number of ways= total number of ways - total number of ways of selecting two friends always,
ways of selecting 6 friends among 10=10C6,
=10!/6!4!=210ways,
total number of selecting two friends always=
2C2×8C4=8!/4!4!=70,
required number of ways=210-70=140
Community Answer
A lady gives a dinner party to 6 guests . The no.of ways in which they...
Let us say two friends A and B among the 10 friends will not attend the party together.
• Case 1: Both A and B didn't attend the party
So, we have to select 6 from the rest 8 friends. It can be done in 8C6 = 28 ways
• Case 2: A attends the party so B won't
Here already A is confirmed to attend, so we have to select 5 more guests from the remaining. But as A is attending B won't attend and we have to exclude him. So, we have to select 5 from the rest 8 guests. It can be done in 8C5 = 56 ways
• Case 3: B attends the party so A won't
Here already B is confirmed to attend, so we have to select 5 more guests from the remaining. But as B is attending A won't attend and we have to exclude him. So, we have to select 5 from the rest 8 guests. It can be done in 8C5 = 56 ways
Total number of ways = 28 + 2(56)
= 140 ways
• Case 1: Both A and B didn't attend the party
So, we have to select 6 from the rest 8 friends. It can be done in 8C6 = 28 ways
• Case 2: A attends the party so B won't
Here already A is confirmed to attend, so we have to select 5 more guests from the remaining. But as A is attending B won't attend and we have to exclude him. So, we have to select 5 from the rest 8 guests. It can be done in 8C5 = 56 ways
• Case 3: B attends the party so A won't
Here already B is confirmed to attend, so we have to select 5 more guests from the remaining. But as B is attending A won't attend and we have to exclude him. So, we have to select 5 from the rest 8 guests. It can be done in 8C5 = 56 ways
Total number of ways = 28 + 2(56)
= 140 ways
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A lady gives a dinner party to 6 guests . The no.of ways in which they may be selected from among 10 friends ,if two of the friends will not attend the party together?
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A lady gives a dinner party to 6 guests . The no.of ways in which they may be selected from among 10 friends ,if two of the friends will not attend the party together? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A lady gives a dinner party to 6 guests . The no.of ways in which they may be selected from among 10 friends ,if two of the friends will not attend the party together? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lady gives a dinner party to 6 guests . The no.of ways in which they may be selected from among 10 friends ,if two of the friends will not attend the party together?.
A lady gives a dinner party to 6 guests . The no.of ways in which they may be selected from among 10 friends ,if two of the friends will not attend the party together? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A lady gives a dinner party to 6 guests . The no.of ways in which they may be selected from among 10 friends ,if two of the friends will not attend the party together? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lady gives a dinner party to 6 guests . The no.of ways in which they may be selected from among 10 friends ,if two of the friends will not attend the party together?.
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