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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
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A person has 8 friends. The number of ways in which he may invite one ...
Solution:
To invite one or more friends to a dinner, the person has two options:
1. He can invite any one of the 8 friends
2. He can invite any two or more friends from 8 friends
Total number of ways in which he may invite one ore more friends to a dinner = (Number of ways to invite 1 friend) + (Number of ways to invite 2 friends) + (Number of ways to invite 3 friends) + ... + (Number of ways to invite all 8 friends)
Number of ways to invite 1 friend = 8
Number of ways to invite 2 friends = 8C2 = 28
Number of ways to invite 3 friends = 8C3 = 56
Number of ways to invite 4 friends = 8C4 = 70
Number of ways to invite 5 friends = 8C5 = 56
Number of ways to invite 6 friends = 8C6 = 28
Number of ways to invite 7 friends = 8C7 = 8
Number of ways to invite 8 friends = 1
Total number of ways = 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 255
Therefore, the correct option is (B) 255.
To invite one or more friends to a dinner, the person has two options:
1. He can invite any one of the 8 friends
2. He can invite any two or more friends from 8 friends
Total number of ways in which he may invite one ore more friends to a dinner = (Number of ways to invite 1 friend) + (Number of ways to invite 2 friends) + (Number of ways to invite 3 friends) + ... + (Number of ways to invite all 8 friends)
Number of ways to invite 1 friend = 8
Number of ways to invite 2 friends = 8C2 = 28
Number of ways to invite 3 friends = 8C3 = 56
Number of ways to invite 4 friends = 8C4 = 70
Number of ways to invite 5 friends = 8C5 = 56
Number of ways to invite 6 friends = 8C6 = 28
Number of ways to invite 7 friends = 8C7 = 8
Number of ways to invite 8 friends = 1
Total number of ways = 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 255
Therefore, the correct option is (B) 255.
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Community Answer
A person has 8 friends. The number of ways in which he may invite one ...
For each friend, the person has two choices: either to invite them or not to invite them. Since there are 8 friends, each with 2 choices, the total number of ways to choose friends (including choosing none) is:
28 = 256
However, since the question specifies "one or more" friends, we subtract the case where no friends are invited.
256-1 = 255
However, since the question specifies "one or more" friends, we subtract the case where no friends are invited.
256-1 = 255
Correct answer: b) 255
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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)250b)255c)200d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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