Prep Questions...please help me

[ankit1383]

Tanya prepared 4 different letters to be sent to 4 different addresses.For each letter,she prepared an envelope with its correct address.If 4 letters are to be put in to 4 envelope at random,what is the probability that only 1 letter will be put in the address with the correct address?

1 1/24
2 1/8
3 1/4
4 1/3
5 3/8

[anniev2]

is the answer 1/8?

[ankit1383]

1/3.....................please explain the answer.............

[Morgoth]

4 envelops, 4 letters

1 right, 3 wrong.

probability first one goes into correct envelop = 1/4
probability second one goes into incorrect envelop = 1-1/3 = 2/3
probability third one goes into incorrect envelop = 1-1/2 = 1/2
the fourth one will automatically will go into incorrect envelop = 1

probability = 1/4*2/3*1/2 = 1/12


Now we have four cases i.e second going into correct, then third one going into correct envelope and lastly fourth one going into correct one.

Thus,

total probability = 1/12 + 1/12 + 1/12 + 1/12 = 4/12 = 1/3

Hope this helps