Question

When a telephone exchange is established, there are 10,000 new phone numbersto use(i.e. 722-0000 to 722-9999). Of these 10,000 phone numbers, how many do not contain the digit "9"?

I know I can do it this long way, but how do I do it in a shorter more reliable way.

722-0000
722-0001
722-0002
722-0003

Ect....
Thank you

Answer 1

with no restrictions, number of 4 digit permutations are
10x10x10x10 = 10,000 as you stated

but , if we exclude the 9, we have only 9 numerals to play with

number of 4 digit phone number endings
= 9x9x9x9 = 6561

(now, a nicer question would have been:
of those 4 digit endings, how many would contain a pair of 9's)

Answer 2

Thank you Reiny.
That makes perfect sense to me. Next time I post a question I will think a little harder to possible ways of working questions like this.
😀😀