Question

Suppose that six guests check their hats when they arrive at the Cigar Parlor and that these hats are returned randomly when they leave. Determine the probability that no guest will receive the proper hat.

Answer 1

Answer:

0.1667

Step-by-step explanation:

There are 6! ways to arrange the hats. The number of ways for which no guest will receive the proper hat is 5! (since there are 5 wrong hats for the first guest, 4 for the second guest, and so on). The probability that no guest will receive the proper hat is:

$P=\frac{5!}{6!}=0.1667$

The probability is 0.1667.