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Hi again Corban, Yes, the answer is $7 \times 7 \times 7.$ As I did above, imagine that the 3 digit arrangements are 3 digit numbers. To list the all start with the leftmost digit. You have 7 choices so your possible one digit numbers are
Now the second digit. Each of the above one digit numbers can be extended to a two digit number by appending any of the digits 1 to 7 in the second place. Thus all possible two digit numbers are
I didn't write them all but you can see that since each one digit number can be extended to a two digit number in 7 ways there are $7 \times 7$ two digit numbers. Finally the third digit. Each of the two digit numbers can be extended to a three digit number by appending and of the digits 1 to 7 in the third place. Hence all possible three digit numbers are
Again I didn't list them all but you can see that since each two digit number can be extended to a three digit number in 7 ways there are $7 \times 7 \times 7 $ three digit numbers. Penny 



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