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.

Most Viewed Questions

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions