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Hello everyone I'm not a mathematician but I love Maths . I have a presentation about a telecom company and I want to know how many numbers exit of 10 digits that have the following prefixes :

0610XXXXXX 0611XXXXXX 0613XXXXXX 0615XXXXXX 0616XXXXXX 0618XXXXXX 0622XXXXXX 0623XXXXXX 0624XXXXXX 0628XXXXXX 0636XXXXXX 0637XXXXXX 0639XXXXXX 0641XXXXXX 0642XXXXXX 0643XXXXXX 0648XXXXXX 0650XXXXXX 0651XXXXXX 0652XXXXXX 0653XXXXXX 0654XXXXXX 0655XXXXXX 0658XXXXXX 0659XXXXXX 0661XXXXXX 0662XXXXXX 0666XXXXXX 0667XXXXXX 0668XXXXXX 0670XXXXXX 0671XXXXXX 0672XXXXXX 0673XXXXXX 0676XXXXXX 0677XXXXXX 0678XXXXXX 0682XXXXXX 0689XXXXXX 0696XXXXXX 0697XXXXXX 0761XXXXXX 0762XXXXXX

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  • $\begingroup$ How many six-digits numbers XXXXXX exists? $\endgroup$
    – Martin R
    Nov 25, 2018 at 14:38
  • $\begingroup$ I want to know how many10 digit numbers exits with the following prefixes but i choose six-digits numbers is way bigger then what i want $\endgroup$
    – Falcon_S
    Nov 25, 2018 at 14:40
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    $\begingroup$ "Way bigger than what you want" is a problem if that's how many six digit numbers there actually are. $\endgroup$
    – Ethan Bolker
    Nov 25, 2018 at 14:41
  • $\begingroup$ @Ethan Bolker What i mean is just for those specific prefixes $\endgroup$
    – Falcon_S
    Nov 25, 2018 at 14:43

1 Answer 1

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For each prefix you have six $X$'s. They form a six digit number (that may start with $0$). How many six digit numbers are there, starting with $000000$ and ending with $999999$?

So there are a million ten digit numbers for eac fixed four digit start. Since you specify $43$ four digit starts, you are talking about $43$ million possible numbers.

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  • $\begingroup$ the numbers of X can be from 0 to 9 with a random way $\endgroup$
    – Falcon_S
    Nov 25, 2018 at 14:41
  • $\begingroup$ Can you please tell how do you find the answer just curiosity ? $\endgroup$
    – Falcon_S
    Nov 25, 2018 at 14:52
  • $\begingroup$ There are $10$ one digit numbers, $100$ two digit numbers, and so on. Each time you add a digit there are $10$ possible choices for that next digit. $\endgroup$
    – Ethan Bolker
    Nov 25, 2018 at 14:55

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