Question

the local seven - digit telephone numbers in city a have 024 as the first three digits. how many different telephone numbers are possible in city a? telephone numbers

Explanation:

Step1: Analyze the fixed and variable parts

The first three digits are fixed as 024. For a seven - digit number, the remaining \(7 - 3=4\) digits can vary. Each of the remaining 4 digits can take values from 0 - 9.

Step2: Use the counting principle

By the fundamental counting principle, if there are \(n_1,n_2,n_3,n_4\) ways to fill each of the 4 remaining digit positions respectively, and \(n_1 = n_2=n_3=n_4 = 10\) (since each digit can be 0 - 9). The total number of ways to form the remaining 4 - digit part is \(n_1\times n_2\times n_3\times n_4\).

$$10\times10\times10\times10=10^{4}$$

Answer:

10000