Concept explainers
In Exercises 45-72, use permutations, combinations, the fundamental counting principle, or other counting methods, as appropriate.
Ordering Performers in a Music Recital A music class of five girls and four boys is having a recital. If each member is to perform once, how many ways can the program be arranged in each of the following cases?
(a) All girls must perform first.
(b) A girl must perform first, and a boy must perform last.
(c) Elisa (a girl) and Doug (a boy) will perform first and last, respectively.
(d) The entire program will alternate between girls and boys.
(e) The first, fifth, and ninth performers must be girls.
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