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Chapter 1: Q. 1.2 (page 19)
If Americans, French people, and British people are to be seated in a row, how many seating arrangements are possible when people of the same nationality must sit next to each other?
The required no. of seating arrangements are.
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A student has to sell books from a collection of math, science, and economics books. How many choices are possible if
(a) both books are to be on the same subject?
(b) the books are to be on different subjects?
How many different letter arrangements can be made from the letters (a) Fluke? (b) Propose? (c) Mississippi? (d) Arrange?
Consider a tournament of contestants in which the outcome is an ordering of these contestants, with ties allowed. That is, the outcome partitions the players into groups, with the first group consisting of the players who tied for first place, the next group being those who tied for the next-best position, and so on. Let localid="1648231792067" denote the number of different possible outcomes. For instance, localid="1648231796484" , since, in a tournament with localid="1648231802600" contestants, player localid="1648231807229" could be uniquely first, player localid="1648231812796" could be uniquely first, or they could tie for first.
(a) List all the possible outcomes when .
(b) With localid="1648231819245" defined to equal localid="1648231826690" , argue without any computations, that localid="1648281124813"
Hint: How many outcomes are there in which localid="1648231837145" players tie for last place?
(c) Show that the formula of part (b) is equivalent to the following:
localid="1648285265701"
(d) Use the recursion to find N(3) and N(4).
A dance class consists of students, of which are women and 12 are men. If men and women are to be
chosen and then paired off, how many results are possible?
John, Jim, Jay, and Jack have formed a band consisting of 4 instruments. If each of the boys can play all 4 instruments, how many different arrangements are possible? What if John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums?
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