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In a group of 267 people how many friends are there who have an identical number of friends in that group?
- a)266
- b)2
- c)138
- d)202
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In a group of 267 people how many friends are there who have an identi...
Given information:
- There is a group of 267 people.
- We need to determine the number of friends who have an identical number of friends in that group.
To solve this problem, we can use the Pigeonhole Principle.
Explanation:
The Pigeonhole Principle states that if we have more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon.
In this context, we can consider each person in the group as a pigeon and the number of friends they have as pigeonholes. Since there are 267 people in the group, each person can have a maximum of 266 friends (excluding themselves).
If every person had a different number of friends, there would be a total of 266 different numbers of friends. However, since there are 267 people, there must be at least one number of friends that is shared by multiple people.
Therefore, the answer is option B) 2, indicating that there are at least two friends who have an identical number of friends in the group.
In other words, there are at least two people in the group who have the same number of friends.
- There is a group of 267 people.
- We need to determine the number of friends who have an identical number of friends in that group.
To solve this problem, we can use the Pigeonhole Principle.
Explanation:
The Pigeonhole Principle states that if we have more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon.
In this context, we can consider each person in the group as a pigeon and the number of friends they have as pigeonholes. Since there are 267 people in the group, each person can have a maximum of 266 friends (excluding themselves).
If every person had a different number of friends, there would be a total of 266 different numbers of friends. However, since there are 267 people, there must be at least one number of friends that is shared by multiple people.
Therefore, the answer is option B) 2, indicating that there are at least two friends who have an identical number of friends in the group.
In other words, there are at least two people in the group who have the same number of friends.
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In a group of 267 people how many friends are there who have an identi...
Suppose each of the 267 members of the group has at least 1 friend. In this case, each of the 267 members of the group will have 1 to 267-1=266 friends. Now, consider the numbers from 1 to n-1 as holes and the n members as pigeons. Since there is n-1 holes and n pigeons there must exist a hole which must contain more than one pigeon. That means there must exist a number from 1 to n-1 which would contain more than 1 member. So, in a group of n members there must exist at least two persons having equal number of friends. A similar case occurs when there exist a person having no friends.
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In a group of 267 people how many friends are there who have an identical number of friends in that group?a)266b)2c)138d)202Correct answer is option 'B'. Can you explain this answer?
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