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) 237I have been asked this question in an international level competition.Enquiry is from Counting in chapter Counting of Discrete Mathematics

There are six movie parts numbered from 1 to 6. Find the number of way

1.	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) 237I have been asked this question in an international level competition.Enquiry is from Counting in chapter Counting of Discrete Mathematics
Answer» 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.

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