Count the number of different 8 letter, English words that do not include the string “bad.”

20. Georgette labels her notebooks with a string of three letters from the set {A,B,X,Y,Z}, and the first two letters in each label must be distinct. (Acceptable: ABA, XYA. Unacceptable:AAX, BBB.) How many different labels are there? (a) 10 (b) 60 (c) 14 (d) 100 (e) 125 (f) none of the above

4. A computer randomly prints a three-digit string of numbers. The string consists only of the digits 0, 1, 2, or 3 and satisfies the extra condition that the sum of its digits is 3. As an example, 021 is one such string. d. After the string of numbers is printed, we randomly select one of the strings three angs Each of the three digits is equally to be chosen. Let G be the event that the digit selected is a 0. This depends on the number of o's in the string that is printed. For example, if the string has two o's, we get the conditional probability P(G|A) = . Using similar logic, write down the conditional probabilities P(GB) and P(GC).

4. A computer randomly prints a three-digit string of numbers. The string consists only of the digits 0, 1, 2, or 3 and satisfies the extra condition that the sum of its digits is 3. As an example, 021 is one such string. a. Write down the sample space s of all such three-digit strings. (HINT: There should be 10 total outcomes including 021. Make sure you found all of them.)