求高手解答一道概率题

tof111

跪求高人，看看这题怎么做
Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
(A) 1/24 (B) 1/8 (C) 1/4 (D) 1/3 (E) 3/8

lilacrabbit

度娘答案
设四封信是abcd,四个信封是ABCD。
先假设A里放a(是正确的），bcd都放在错误的信封里，有两种情况（CDB,DBC)
这样的情况有A里放a，B里放b,C里放c,D里放d 四种情况 是2*4=8

答案就是：8/4!=1/24=1/3