Question

There are six movie parts numbered from 1 to 6. Find the number of ways in which they be arranged so that part-1 and part-3 are never together.

(a) 876

(b) 480

(c) 654

(d) 237

I have been asked this question in an international level competition.

Enquiry is from Counting in chapter Counting of Discrete Mathematics

Answer 1

Correct answer is (b) 480

Explanation: The total number of ways in which 6 part can be arranged = 6! = 720. The total number of ways in which part-1 and part-3 are always together: = 5!*2! = 240. Therefore, the total number of arrangements, in which they are not together is = 720 − 240 = 480.