Question

Three letters, each of which corresponds to an envelope, are placed in the envelopes at random.

The probability that all the letters are not placed in the right envelopes, is

• A. $\frac{1}{6}$
• B. $\frac{5}{6}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B

$\frac{5}{6}$

Explanation for the correct answer.

Given: Three letters and three envelopes

For the first envelope, we can put one of the letters from three, so we have three ways for the first.

For the second envelope, we have two letters, so we have two ways for a second envelope.

For the third envelope, we have only one letter, so only on way. Therefore the total number of ways is six.

The total numbers of ways that three letters are placed in the envelopes are $3!=6$

There is only one way we can put all the letters in their respective envelopes.

Number of ways that all the letters are on the right envelope $=\frac{1}{6}$

Probability $=\frac{Numberoffavourableevents}{Totalpossibleevents}$

Number of ways that no letter is in the right envelope $=1-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}$

Hence option (B) is correct.