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Let S be the set of all 7-digit numbers which do not contain 0 in any...

Let S be the set of all 7-digit numbers which do not contain 0 in any place — that is,
each element of S is a string of 7 digits with each digit chosen from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}.
How many elements of S are there that don’t contain the substring 123? To qualify as having
123 as a substring, the numbers 1, 2 and 3 must appear in order and consecutively. For instance
“2341234” contains “123” as a substring but “2341243” does not, and neither does “3219999”.
Justify your answer.

Detailed answer with all steps please. Thanks!
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Sol from Total ways to create 7 digit number (1,2,. g} with repeatation allowed -] is Lao al Sways to To exclude those which

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