Question

A u.s. social security number is a nine-digit number. the first digit(s) may be 0. how many have exactly one didgit equal to 8

Answer 1

Think of the SS numbers as being a collection of digits.  If any of the digits (say the first one for example) are 8 then all the remaining digits can be anything but 8, meaning there are 9 choices for each remaining digit.  This effectively becomes an 8 digit number with the constraint that there can only be 9 choices for a digit.  This means for the first digit being 8 we have 9⁸ remaining possible numbers. Since we will do this for each of the remaining digits (they each get to be 8 then we count their 9⁸ configurations) we end up with 9(9⁸) or 9⁹≈3.8742E8