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

Answer:

The probability that only 1 letter will be put into the envelope with its correct address is

Step-by-step explanation:

Given:

Number of Letters=4

Number of addresses= 4

To Find:

The probability that only 1 letter will be put into the envelope with its correct address=?

Solution:

Let us assume first letter goes in correct envelope and others go in wrong envelopes, then

=> Probability putting the first letter in correct envelope =

=>  Probability putting the second letter in correct envelope =

=>  Probability putting the third letter in correct envelope=

=> Probability putting the fourth letter in correct envelope = 1;  

( only 1 wrong addressed envelope is left);

This event can occur with other 3 envelopes too.

Hence total prob. =

=>

so, converting firstly the mixed fractions to improper fractions and then "adding".