Well honey, to arrange 1234567, you just gotta do some basic math. Since you have 7 numbers to work with, you can arrange them in 7! ways, which is 5040. So, there you have it, 5040 ways to shake up those digits.
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Oh, dude, arranging numbers is like playing a really boring game of Sudoku. So, to answer your question, there are 7 factorial ways to arrange 1234567, which is 5040. But like, who has time to sit there and write out all those combinations anyway?
120
120 ways
In 1,307,674,368,000, or 15! ways.
How many different ways can we arrange 9 objects taken 3 at a time?
8