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Chapter 1: Q. 1.14 (page 16)
How many -card poker hands are there?
Number of -card poker hands.
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Consider -digit numbers where each digit is one of the integers . How many such numbers are there for which
(a) no two consecutive digits are equal?
(b) appears as a digit a total of times, ?
The following identity is known as Fermat鈥檚 combinatorial identity:
Give a combinatorial argument (no computations are needed) to establish this identity.
Hint: Consider the set of numbers through . How many subsets of size have as their highest numbered member?
An elevator starts at the basement with people (not including the elevator operator) and discharges them all by the time it reaches the top floor, number. In how many ways could the operator have perceived the people leaving the elevator if all people look alike to him? What if the people consisted of men and women and the operator could tell a man from a woman?
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?
An art collection on auction consisted of Dalis, van Goghs, and Picassos. At the auction were 5 art collectors. If a reporter noted only the number of Dalis, van Goghs, and Picassos acquired by each collector, how many different results could have been recorded if all of the works were sold?
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