Other Topics Puzzle – Challenge 98
Time to challenge and tease your brain with another great math puzzle. Let's see if you can solve it. The solution is also provided.
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 – 240 = 480
Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.
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