Let be the set of consecutive integers and be the set of consecutive integers How many different integers are in or
How many triples of positive integers are there such that
Famous musicians Kay-Zed and Beeta teamed up to do a concert together. During the concert, Kay-Zed played of his greatest hits, and Beeta played of her greatest hits. For an Encore performance, they are going to come out and perform a song together.
They will either perform one of Kay-Zed's greatest hits that he did not already perform, or one of Beeta's greatest hits that she did not already perform, or one from a list of other songs that the fans requested. How many choices for which song to perform do Kay-Zed and Beeta have?
A derangement of a string of distinct elements is a rearrangement of the string such that no element appears in its original position. For example, is a derangement of .
Find the number of all the derangements of .
A number is picked randomly from to and then another number is picked from to regardless of the first pick. If the first pick is the ten's digit of a two-digit number and the second pick is the units digit, how many cases are there such that the two-digit number is less than