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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.
If E has written 300 books. These books are distributed equally among his respective friends by him. Each of his friend further distributes equal amount of books to his/her friend. Also it is known that among his friends, 1 is male and the remaining are females. In how many ways female friends of E can distribute 1 book to their friends more than that by the male friends?
100
120
130
115
None of these
Let's break down the statements and the options:
- E has 3 friends. Out of these, 1 is male and 2 are female.
- E wrote 300 books. Divided equally among 3 friends, each gets 100 books.
- Each friend of E has 5 friends.
Now, if the female friends give 1 book more to each of their 5 friends than the male does, think:
- Let the male friend give x books to each.
- Then, each female gives (x+1) books to each of their 5 friends.
- Total books by male: 5x.
Total books by one female: 5(x+1).
- Since each friend receives all 100 books:
For male: 5x = 100 ? x = 20.
For female: 5(x+1) = 100 ? x+1 = 20 ? x = 19.
- This is not possible, as x cannot have two values at the same time. But let's see if the distribution can be assigned in another way.
- However, the question is about ways the females can distribute 1 more book to each of their friends than the male.
Ways:
- For each female (there are 2), the 5 friends can get the books in any order, but if each must get one more than the male's friends, it's fixed per person.
- However, the number of ways is permutations of distributing the books to the friends.
- For each female: ways = number of arrangements = 5! = 120.
- Total ways = for two females: nothing more to multiply, since the assignment is fixed, unless order matters between females.
- But if it's distribution to friends, and both females do independently, then it's 120 ways for each.
So, Option 2: 120 is correct.
Correct Answer:
- Option 2, 120
By: Parvesh Mehta ProfileResourcesReport error
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