Interesting GMATFix Problem-38

Is it B... 1/60 ?

Can you please provide an explanation for this problem? What would the answer be?
Thanks!

arora007 wrote:Five people wrote down their names on five pieces of paper, and put the pieces in a bag. If each person then randomly took out one piece of paper, what is the probability that exactly 2 people took the pieces with their names on them?
A)1/120
B)1/60
C)1/30
D)1/12
E)1/6

P(1st person chooses his name) = 1/5 (5 names in the bag, 1 correct)
P(2nd person chooses his name) = 1/4 (4 names left, 1 correct)
P(3rd person doesn't choose his name) = 2/3 (3 names left, 2 incorrect)
P(4th person doesn't choose his name) = 1/2 (2 names left, 1 incorrect)
P(5th person doesn't choose his name) = 1/1 (1 name left, and it's incorrect because the correct name has already been chosen)

Since we want all of these events to happen together, we multiply the fractions:

1/5 * 1/4 * 2/3 * 1/2 * 1/1 = 1/60

Since any 2 of the 5 people could choose the correct names, we need to multiply by the number of combinations of 2 that can be made from 5 choices = 5C2 = 10:

10 * 1/60 = 1/6.

The correct answer is E.