Let X be the set of 10-digit numbers that do not contain all digits 0 through 9 in their decimal representation and do not begin with 0. How many elements does the set X have?

I think this should be done by counting principle. So I have 10 spots, and 10 options for each spot. However, the first number can't be 0, so the first spot has 9 options.

9 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 9

I think the 10th spot only have 9 options since I can't repeat one number (the representation doesn't have all the digits).

I think this should be done by counting principle. So I have 10 spots, and 10 options for each spot. However, the first number can't be 0, so the first spot has 9 options.

9 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 9

I think the 10th spot only have 9 options since I can't repeat one number (the representation doesn't have all the digits).