Computer Science

Download Applied Discrete Structures by Alan Doerr, Kenneth Levasseur PDF

By Alan Doerr, Kenneth Levasseur

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If any structure or restriction is placed on the way the social committee is to be selected, the number of possible committees will probably change. For example, if the club has a rule that the treasurer must be on the social committee, then the 24232221 number of possibilities is reduced to 24 = 10626. 4 = 4! If we further require that a chairperson other than the treasurer be selected for the social committee, we have 24 4 · 4 = 42504 different possible social committees. The choice of the four non-treasurers accounts for the factor 24 4 while the need to choose a chairperson accounts for the 4.

The reader is encouraged to visualize the tree diagram of this example, but not to draw it! We formalize the procedures developed in the previous examples with the following rule and its extension. 2 The Rule Of Products: If two operations must be performed, and If the first operation can always be performed p1 different ways and the second operation can always be performed p2 different ways, then there are p1 p2 different ways that the two operations can be performed. Note: It is important that p2 does not depend on the option that is chosen in the first operation.

How many subsets of {1, 2, 3, . . , 10} contain at least seven elements? 4. The congressional committees on mathematics and computer science are made up of five congressmen each, and a congressional rule is that the two committees must be disjoint. If there are 385 members of congress, how many ways could the committees be selected? 5. Expand (2x 3y)4 . 6. Find the fourth term of the expansion of (x 2y)6 . 7. (a) A poker game is played with 52 cards. How many “hands” of five cards are possible?

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