Statistics help

How many different 3 digit identification tags can be made if
a) the digits can be used more than once?
b) the first digit must be 5 and repetitions are not permitted

I wish you would show some attempt to do these yourself. If you know the basic ideas, these are not very difficult questions.

How many different 3 digit identification tags can be made if
a) the digits can be used more than once?

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There are 10 possible digits for each place so \(\displaystyle 10^3= 1000\) possible combinations. (well, yes, 000 to 999)

b) the first digit must be 5 and repetitions are not permitted

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There is obviously just the one possible first digit, 5, and then, because that cannot be repeated, 9 possible digits for the second. Since we cannot use either 5 or whatever digit we used for the second, there are only 8 possible digits for the third. There are 9(8)= 72 possible tags.