Chapter 9.7, Problem 42E

(a)

To determine

To find:The probability that only one paycheck is inserted in correct envelope

Answer to Problem 42E

The probability is $\frac{3}{8}$ .

Explanation of Solution

The total number of ways is,

  $5!=120$

The number of ways to fill one correct envelope is,

  $5\cdot 3\cdot 3\cdot 1=45$

So, the probability is,

  $\begin{array}{c}P=\frac{45}{120}\\ =\frac{3}{8}\end{array}$

So, the probability is $\frac{3}{8}$ .

(b)

To determine

To find:The probability that at least one paycheck is inserted in correct envelope

Answer to Problem 42E

The probability is $\frac{19}{30}$ .

Explanation of Solution

The total number of ways is,

  $5!=120$

The number of ways to fill at least one correct envelope is,

  $\begin{array}{c}1{+}^5{C}_3{+}^5{C}_2\cdot 2+5\cdot 3\cdot 3\cdot 1=1+10+20+45\\ =76\end{array}$

So, the probability is,

  $\begin{array}{c}P=\frac{76}{120}\\ =\frac{19}{30}\end{array}$

So, the probability is $\frac{19}{30}$ .