Question

How many strings of 12 decimal digits begin with "248" or consist only of even digits?

Answer 1

We need to find the number of strings in each of the two cases and then subtract the number that are in both. That is Event A or Event B = Event A + Event B - Event A and B. For strings starting with "248", the remaining 9 digits each have 10 possible values(0-9), so there are 9^10 such strings. For only even digit strings, each of the 12 digits has five possible values(0,2,4,6,8), so there are 12^5 such strings. Only even digit strings starting with "248" would have five possible values for the remaining 9 digits, so there are 9^5 such strings. There for the number of strings of 12 digits beginning with "248" or consisting of only even digits is 9^10+12^5-9^5, or 3,486,974,184 strings.