Ellen invites 5 people to dinner, 2
women and 3 men. If Ellen's dining table is circular and the guests choose
their seats at random around her table, what is the probability that no female
is seated next to another female?

(A) 1/90 (B) 1/72 (C) 5/72 (D) 5/36 (E) 1/10

(A) 1/90 (B) 1/72 (C) 5/72 (D) 5/36 (E) 1/10

Solution follows here:

__Solution:__
Including Ellen there are 6 people – 3 Men and
3 women

Circular permutations concept is explained in a
post on this blog with the following link:

“’n’ persons can be arranged around a circular path
in (n-1)! ways”

Number of all possibilities = (6-1)! = 5!

First arrange 3 men around the table
in (3-1)! = 2! Ways. Then the left out places in between the men are three.
These 3 places can be filled by three women in 3P3 = 3! Ways => number of desired
possibilities = 2!*3!

Probability = number
of desired possibilities / number of all possibilities = 2!*3! / 5!

= 2 / 5*4 = 1/10

**Answer (E)**
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