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In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

/ Mathematics Mcqs, Permutations and Combinations / By
In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

A. 9
B. 12
C. 14
D. 18
Explanation:
The number of arrangement in which A and B are not together
= Total number of arrangements
= Number of arrangements in which A and B are together =4!-3!x2! = 24-12 =12.