Permutation-Combination
Aptitude

 Back to Questions
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.

$4 × 3^5$

 Hide Ans

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, 

$= 4×3×3×3×3×3$

$= 4 × 3^5$


(0) Comment(s)