$$ In each part, $($i$)$ draw the tree that shows only the allowed answers, $($ii$)$ write out the list, and

$($iii$)$ say how many items are on your list.

$($a$)$ Three character strings where each character is a letter, either A$,$ B$,$ or C$.$ Note that repeats like AAB are allowed.

$($b$)$ All such strings if repeats are allowed, but not in a row. ABA is acceptable, but AAB is not.

$($c$)$ All such strings if no repeats are allowed, meaning each of $A,B,$ or $C$ is used once.

$$ In each part, $($i$)$ draw the tree that shows only the allowed answers, $($ii$)$ write out the list, and $($iii$)$ say how many items are on your list.

$($C$)2016$ Suzanne Dor$$e$,$ Augsburg College. For more information contact:

doree@augsburg.edu

$($a$)$ All bit strings of length four.

$($b$)$ Bit strings of length four that contain exactly two $0s.$

$($c$)$ Bit strings of length four that contain one or two $0$s$.$

My favorite cafe offers three types of soup and five types of salad.

$($a$)$ How many choices are there if I have a soup and then a salad? Which of Cases or Steps could be used to find the answer? Explain how.

$($b$)$ How many choices are there if I choose one soup or one salad $($but not both$)?$ Which of Cases or Steps could be used to find the answer? Explain how.

$($c$)$ How many choices are there if I have a soup or salad to start and then the other as my main course? Show how to find the answer by splitting into two cases of two steps each.