Chapter 9.7, Problem 43E

(a)

To determine

To find:The probability that guess the position of each digit.

Answer to Problem 43E

The probability is $\frac{1}{120}$ .

Explanation of Solution

There is 1 way to guess all positions correctly out of total ${}^5{P}_5$ ways so, probability is calculated as,

  $\begin{array}{c}\frac{1}{{}^5{P}_5}=\frac{1}{5!}\\ =\frac{1}{120}\end{array}$

So, the probability is $\frac{1}{120}$ .

(b)

To determine

To find:The probability that know the position of first digit and guess the position of each digit.

Answer to Problem 43E

The probability is $\frac{1}{24}$ .

Explanation of Solution

There is 1 way to guess all positions correctly out of total ${}^4{P}_4$ ways so, probability is calculated as,

  $\begin{array}{c}\frac{1}{{}^4{P}_4}=\frac{1}{4!}\\ =\frac{1}{24}\end{array}$

So, the probability is $\frac{1}{24}$ .