Other Topics Puzzle – Challenge 98

Challenge:

In how many ways can Ann, Bea, Cam, Don, Ella and Fey be seated on a straight line if Ann and Bea cannot be seated next to each other?

A- 240

B- 360

C- 480

D- 620

E- 720

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The formula for N people to sit in a straight line is N! and at a round table there is (n-1)!.
There are six people. So, the number of different ways to sit them is 6! = 720
From these 720 ways, we must subtract the number of ways that Ann and Bea can sit next to each other.
The cases we need to subtract from whole are the ways of seating 5 persons and one “pair”. That would be 5! or 5 × 4 × 3 × 2 × 1 = 120
However, there are two ways Ann and Bea could sit, Ann left of Bea or Bea left of Ann.
So, we double 120 ways to 240 ways.
Answer: 720 – 240 = 480