Question

A mail-sorting clerk is given 4 envelopes addressed to different people and 4 letters. She has to carefully put the letters in the correct envelopes and then mail them. However, she carelessly puts any letter in any envelope, making sure that each envelope has precisely one of those 4 letters. What is the likelihood that all the letters are in the correct envelope?

• A. 1/24
• B. 1/12
• C. 1/6
• D. 1/4

Answer 1

Answer: (A)

1/24

Answer 2

Since there are 4 envelopes and each letter must go into one envelope, the total number of ways to arrange the letters into envelopes is the number of permutations of 4 letters. This is given by:

$4!=244!$

Favorable outcomes (correct arrangement):

There is only 1 correct arrangement in which all the letters are in their correct envelopes.

Probability:

The probability is the ratio of favorable outcomes to total possible outcomes:
$\frac{1}{24}$
The correct answer is (A) : 1/24