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Comprehension

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?


1. 100
2. 120
3. 130
4. 115
5. None of these

1 Answer

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Correct Answer - Option 2 : 120

Number of ways 1 female can distribute the books her 5 friends = 5!

So, Number of ways 2 females can distribute the books their friends = 2 × 5!

Number of ways male can distribute 1 book to his 5 friends = 5!

Difference between number of ways = (2 × 5!) - 5!

⇒ 5!

⇒ 5 × 4 × 3 × 2 × 1

⇒ 120 ways

∴ In 120 ways female friends of E can distribute 1 book to their friends more than that by the male friends.

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