Daniel and Celine are part of a group having 8 students. there are 8 chairs arranged on a stage in a straight line. this group of students must sit on these 8 chairs. Daniel cannot sit next to Celine. how many arrangements are possible?
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No. of ways to seat 7 entities = 7!
Total number of ways all members can sit = 8!
Since they can be seated (together) as one entity as either DC or CD.
So number of ways they can sit apart = 8!-2*7!
There are 6! possible permutations of the 6 students with Daniel and Celine excluded.
When Daniel and Celine are included in each of the 6! permutations, there are 6 * 7 ways of including Daniel and Celine without seating them together.
Therefore the total possible number of seating arrangements = 6 * 7 * 6! = 6 * 7!