A bookshelf can accommodate 6 books from left to right. If 8 identical books on each of the languages A, B, C and D are available, in how many ways can the bookshelf be filled such that books of the same language are not put adjacent to each other?

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Solution

The correct option is C

A book of a particular language can be chosen in 4 ways.

If that particular book occupies 1 space on the bookshelf, there are 3 possible selections of other books in each of the remaining 5 spaces.

$∴$ The number of arrangements that can be done = $4 \times$ $3^{5}$

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A bookshelf can accommodate 6 books from left to right. If 8 identical books on each of the languages A, B, C and D are available, in how many ways can the bookshelf be filled such that books of the same language are not put adjacent to each other?

The correct option is C A book of a particular language can be chosen in 4 ways. If that particular book occupies 1 space on the bookshelf, there are 3 possible selections of other books in each of the remaining 5 spaces. ∴The number of arrangements that can be done = 4× 35

The correct option is C

A book of a particular language can be chosen in 4 ways.

If that particular book occupies 1 space on the bookshelf, there are 3 possible selections of other books in each of the remaining 5 spaces.

$∴$ The number of arrangements that can be done = $4 \times$ $3^{5}$