Wednesday 16 November 2011

Probability-11 (GMAT)

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
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)

No comments:

Post a Comment