Other Topics Puzzle – Challenge 98
Other Topics Puzzle – Challenge 98 asks how many ways six people can sit in a line if two of them cannot sit together. The quick route is to count all the arrangements, then subtract the ones where the pair is adjacent — treating that pair as a single block.
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 correct answer is C.
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 to 240 = 480
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