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Read the following lines and answer the questions that follow: -
There are a total of 5 different writers – A, B, C, D and E. They write their books and distribute them among their friends. It is also known that none of these friends are mutual with respect to each other. Also the following information is available:
(i) A has a total of 7 friends. Each of his friends has 4 friends.
(ii) B has a total of 5 friends. Each of his friends has 3 friends.
(iii) C has total of 4 friends. Each of his friends has 5 friends.
(iv) D has total of 6 friends. Each of his friends has 2 friends.
(v) E has total of 3 friends. Each of his friends has 5 friends.
In how many ways the friends of A exchange their 1 book with each other?
20
32
30
28
None of these
Let’s make this simple:
- There are five writers: A, B, C, D, E. Each has a certain number of friends.
- A has 7 friends, each friend knows 4 other people (but those 4 are different from each other's friends).
- The question: In how many ways can A’s 7 friends exchange 1 book with each other?
- Since each friend can give/receive with 6 others, but exchanges are mutual, we just care about friend-to-friend swaps.
- In math terms, it’s the number of ways to choose 2 people out of 7 to swap books:
- That's just “7 choose 2” = 7 × 6 / 2 = 21.
Now, your options:
Option 1: 20
Option 2: 32
Option 3: 30
Option 4: 28
Option 5: None of these
The correct answer is 21, which isn’t even listed. It’s not 28. The answer choices may have been misprinted, but either way:
What this really means: For this kind of pairwise swapping where each friend only swaps once with another, it comes down to the combinations formula. Always “n choose 2” for the number of possible swaps among n people. So for 7 friends, it should be 21. If 21 isn’t listed, then the right option should be “None of these.”
By: Parvesh Mehta ProfileResourcesReport error
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