A bookshelf can accommodate 6 books from left to right. If 10 identical books on each of the languages - French, German, Spanish and English are available, in how many ways can the bookshelf be filled such that books on the same language are not put adjacently?

  • Option 1)


  • Option 2)

    10 x 95

  • Option 3)


  • Option 4)

    4 x 35


Answers (1)

As learnt in concept

Number of Permutations without repetition -

Arrange n objects taken r at a time equivalent to filling r places from n things.


- wherein

Where r\leq n\ \; and\; \; r\geq 0


 B_1 can be filled in 4 four ways.

B_2, B_3, B_4,B_5,B_6 can be filled in 3 ways each.

Since the books cannot be similar, Thus,




Option 1)


Incorrect option

Option 2)

10 x 95

Incorrect option

Option 3)


Incorrect option

Option 4)

4 x 35

correct option

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