Chapter 13.9, Problem 40STP

To determine

To calculate: To find how many seven-digit phone are available

Answer to Problem 40STP

The number of seven digit phone numbers available are $483840$

Explanation of Solution

Given information: Seven digit phone numbers if a digit can be used only once and the first digit cannot be zero or one

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

  $\mathrm{Probability}=\frac{Event}{Outcomes}$

Calculation:

Given seven digit phone numbers if a digit can be used only once and the first digit cannot be zero or one

Number of digits $=10$

Number of digits possible at each place starting from left

_8_ _9_ _8__7__6__5__4__3_

Hence, total number of seven digit phone numbers is calculated as

  $\begin{array}{l}Number=8\times 9\times 8\times 7\times 6\times 5\times 4\\ Number=483840\end{array}$

Conclusion:

Hence, number of seven digit phone numbers available are $483840$