Question

Andrew and Lindsey are seated at a round table with four other people. If everyone is randomly seated, what is the probability that Andrew and Lindsey are seated next to each other? Express your answer as a common fraction.

Answer 1

2/5  is the probability that Andrew and Lindsey are seated next to each other

Step-by-step explanation:

Andrew and Lindsey are seated at a round table with four other people

Total 6 People

on Circular table total arrangements = (6-1) ! = 5!

Now taking

Andrew and Lindsey  as one , they can be seated in 2 ways

Total = 4 Other  + 1(Andrew and Lindsey ) = 5

number of Ways Andrew and Lindsey sitting together = 2 * (5 - 1)! = 2 * 4!

probability that Andrew and Lindsey are seated next to each other

=  2 * 4! / 5!

= 2/5

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Answer 2

The probability that Andrew and Lindsey are seated next to each other is 2/5.

Step-by-step explanation:

Consider the provided information.

Andrew and Lindsey are seated at a round table with four other people.

That means there are 6 people.

Total ways to sit at a round table by 6 people = (n-1)! = (6-1)! = 5! ways

Total number of ways to sit at round table when Andrew and Lindsey sitting next to each other will be counted by taking Andrew and Lindsey  as one person and they can sit next to each other by two ways either Lindsey be on right side of Andrew or left side of Andrew.

Total number of ways to sit at round table when Andrew and Lindsey sitting next to each other = $(5-1)!\times2! = 4! \times 2$

Thus the required probability is = $\frac{4! \times 2}{5!}=\frac{2}{5}$

Hence, the probability that Andrew and Lindsey are seated next to each other is 2/5.

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