Question

A stockroom clerk returns three safety helmets at random to three steel
mill employees who had previously checked them. If Smith , Jones, and
Brown, in that order, receive one of the three hats, list the sample space
points for the possible orders of returning the helmets, and find the
value m of the random variable M that represents the number of incorrect
matches.

Answer 1

If S, J, and B stand for Smith’s, Jones’s, and Brown’s helmets, respectively, then the possible arrangements in which the helmets may be returned and the number of correct matches are

$$\{SJB, SBJ, JSB, JBS, BSJ, BJS\}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} Sample\ Space & m \\ \hline SJB & 3 \\ \hdashline SBJ & 1 \\ \hdashline JSB & 1 \\ \hdashline BJS & 1 \\ \hdashline JBS & 0 \\ \hdashline BSJ & 0 \\ \end{array}$$