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A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is. (a) 250 (b) 255 (c) 200 (d) none of these?
Most Upvoted Answer
A person has 8 friends. The number of ways in which he may invite one ...
Solution:
The person can invite one friend or two friends or three friends and so on up to all eight friends.
The number of ways to invite one or more friends is the sum of the number of ways to invite one friend, two friends, three friends, up to eight friends.
Let's calculate each of these:
- Inviting one friend: The person can choose one friend out of eight in 8 ways.
- Inviting two friends: The person can choose two friends out of eight in 8C2 = 28 ways.
- Inviting three friends: The person can choose three friends out of eight in 8C3 = 56 ways.
- Inviting four friends: The person can choose four friends out of eight in 8C4 = 70 ways.
- Inviting five friends: The person can choose five friends out of eight in 8C5 = 56 ways.
- Inviting six friends: The person can choose six friends out of eight in 8C6 = 28 ways.
- Inviting seven friends: The person can choose seven friends out of eight in 8C7 = 8 ways.
- Inviting eight friends: The person can choose all eight friends in 1 way.
Therefore, the total number of ways in which the person may invite one or more of his friends to a dinner is:
8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 255
Hence, the correct answer is (b) 255.
The person can invite one friend or two friends or three friends and so on up to all eight friends.
The number of ways to invite one or more friends is the sum of the number of ways to invite one friend, two friends, three friends, up to eight friends.
Let's calculate each of these:
- Inviting one friend: The person can choose one friend out of eight in 8 ways.
- Inviting two friends: The person can choose two friends out of eight in 8C2 = 28 ways.
- Inviting three friends: The person can choose three friends out of eight in 8C3 = 56 ways.
- Inviting four friends: The person can choose four friends out of eight in 8C4 = 70 ways.
- Inviting five friends: The person can choose five friends out of eight in 8C5 = 56 ways.
- Inviting six friends: The person can choose six friends out of eight in 8C6 = 28 ways.
- Inviting seven friends: The person can choose seven friends out of eight in 8C7 = 8 ways.
- Inviting eight friends: The person can choose all eight friends in 1 way.
Therefore, the total number of ways in which the person may invite one or more of his friends to a dinner is:
8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 255
Hence, the correct answer is (b) 255.
Community Answer
A person has 8 friends. The number of ways in which he may invite one ...
2^8-1= 256-1
255 option (b) is answer
255 option (b) is answer
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A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is. (a) 250 (b) 255 (c) 200 (d) none of these?
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A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is. (a) 250 (b) 255 (c) 200 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is. (a) 250 (b) 255 (c) 200 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is. (a) 250 (b) 255 (c) 200 (d) none of these?.
A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is. (a) 250 (b) 255 (c) 200 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is. (a) 250 (b) 255 (c) 200 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is. (a) 250 (b) 255 (c) 200 (d) none of these?.
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