How many ways we can arrange A,B,C,D letters so that AB,BC,CD should not be together

Answers (1)

The letters A,B,C,D can be arranged in 4! ways.
Total possible ways of arranging the letters are 4!=24
In order to calculate neither a and b nor c and d come together,first we have to see the cases when they do come togther
So we take a and b as a single element,due to which the total elements are now 3
	herefore 3 letters can be arranged in 3! ways and a and b itself can be arranged in 2!.
Cases when a and be are together can be arranged in 3!*2! ways
i.e,3!*2!
ightarrow3*2*1*2*1=12: ways
Similarly for the case when c and d are together i.e, 12 ways.
Now the case when a and b and c and d are together,the case becomes
2!*2!*2!=2*2*2=8 ways
So the total number of ways when neither of them are together are
=24-12-12+8=8
Hence there are 8 number of ways when letters a b c and d can be arrange in which neither of them are together.

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