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?

Answers (1)

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,

4*3*3*3*3*3=4*3^{5}

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