# Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. A book-shelf can accommodate 6 books from left to right. If 10 identical books on each of the languages $A,B,C$ and $D$ are available, In how many ways can the book shelf be filled such that book on the same languages are not put adjacently.
 ✖ A. $\dfrac{^{40}P_6}{6!}$ ✖ B. $10 × 9^5$ ✖ C. $\dfrac{^6P_4}{2!}$ ✔ D. $4 × 3^5$

Solution:
Option(D) is correct

First place can be filled in 4 ways. (Since any book of the languages $A,B,C$ and $D$ can be put)

The subsequent places can be filled in 3 ways each. (Since the other three language books can be placed but not the book of the same language)

Hence, the number of ways,

$= 4×3×3×3×3×3$

$= 4 × 3^5$