discrete math

How many strings of four decimal digits (Note there are 10 possible digits and a string can be of the form 0014 etc., i.e., can start with zeros.)
(a) have exactly three digits which are 9s?

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  1. Think of 3 9's to which we have to insert a fourth digit x(which is not a nine).

    This can be in the four following ways.
    X999 or 9X99 or 99X9 or 999X
    In each case X can represent 9 possible digits including 0 but excluding 9.

    So the number of strings is 4*9=36.

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