Probability Question

[ayashlaha]

1.) There are 4 letters and 4 corresponding envelopes. If we put the 4 letters into the envelopes at random, what is the probability that only one letter was into the exact envelope?


A) 1/8

B) 1/6

C) 1/3

D) 1/2

E) 3/4

I dont know the official answer but cannot get the right solution. any help will be greatly appreciated.

[sanjana]

P(only 1 letter in the correct envelope) =

P(1st correct and 2,3,4 in wrong) OR
P(2nd correct and 1,2,3 in wrong) OR
P(3rd correct and 1,2,4 in wrong) OR
P(4th correct and 1,2,3 in wrong)

P(1st correct) = 1/4 (1 correct out of 4 envelopes)
P(2nd wrong) = 2/3
P(3rd wrong) = 1/2
P(4th wrong) = 1/1

Hence,P(1st correct and 2,3,4 in wrong) = 1/4*2/3*1/2 = 1/12

Same will be the probability for the other 3 cases
Hence required Probaboility = 4*1/12 = 1/3.