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)

    \frac{40P_{6}}{6!}

  • Option 2)

    10 x 95

  • Option 3)

    \frac{6P_{4}}{2!}

  • 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,

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

 

 


Option 1)

\frac{40P_{6}}{6!}

Incorrect option

Option 2)

10 x 95

Incorrect option

Option 3)

\frac{6P_{4}}{2!}

Incorrect option

Option 4)

4 x 35

correct option

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