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Magazine Problem 1
In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?
Problem 1
Find the expansion of \((x+y)^{4}\) a) using combinatorial reasoning, as in Example \(1 .\) b) using the binomial theorem.
Problem 1
Place these permutations of \(\\{1,2,3,4,5\\}\) in lexicographic order: \(43521,15432,45321,23451,23514,\) \(14532,21345,45213,31452,31542\)
Problem 1
List all the permutations of {a, b, c}.
Problem 1
There are 18 mathematics majors and 325 computer science majors at a college. a) In how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? b) In how many ways can one representative be picked who is either a mathematics major or a computer science major?
Problem 1
Show that in any set of six classes, each meeting regularly once a week on a particular day of the week, there must be two that meet on the same day, assuming that no classes are held on weekends.
Problem 2
An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building?
Problem 2
Find the expansion of \((x+y)^{5}\) a) using combinatorial reasoning, as in Example \(1 .\) b) using the binomial theorem.
Problem 2
In how many different ways can five elements be selected in order from a set with five elements when repetition is allowed?
Problem 2
Show that if there are 30 students in a class, then at least two have last names that begin with the same letter.
