Chapter 8, Problem 8.70RE

To determine

To calculate the probability that Nick’s phone number contains no repeated digits.

Answer to Problem 8.70RE

The probability is $0.06048$ .

Explanation of Solution

To find out the number of phone numbers that contain no repeated digits using multiple counting principle and the fact that there are ten digits:

  $\begin{array}{l}8\times 7\times 6\times 5\times 4\times 3\times 2\\ =483,840\end{array}$

In the previous exercise we noted that $8,000,000$ telephone numbers were possible.

The probability is then:

  $\begin{array}{l}\frac{483,840}{8,000,000}\\ =0.06048\\ =6.048\%\end{array}$

Hence the answer.