Question

A 7-digit telephone number has the form abc - xxxx, where x, b, and c can be any digit 1 - 9 and a is restricted to 3 - 9. how many numbers are possible?

Answer 1

The total 7-digit telephone numbers has the form abc-xxxx which are possible are 3,720,087

It is given that,

A 7-digit telephone number has the form = abc - xxxx

Also,  x, b, c can have any digit between 1-9

And, a is restricted to between 3-9

We need to find the possible number of combinations of a 7-digit telephone number having the form abc-xxxx

Then, number of digits that can be placed at the place of 'a' = 7 type of digits (3 to 9)

Number of digits that can be placed at the place of x, b and c= 9 type of digits (1 to 9)

Suppose, we put a number from 3 to 9 at 'a', so total possibilities are 7

Similarly, at 'b' we put a number from 1-9, so total possibilities are 9 and so on so forth  

Thus total 7-digit telephone numbers which have the possible combinations can be

= 7*9*9*9*9*9*9

= 3,720,087

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