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Chapter 11: Problem 49
An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?
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A fair coin is tossed two times in succession. The sample space of equally likely outcomes is \(\\{H H, H T, T H, T T\\} .\) Find the probability of getting $$\text{two heads.}$$
Exercises \(116-118\) will help you prepare for the material covered in the next section. In Exercises \(116-117\) show that $$1+2+3+\cdots+n=\frac{n(n+1)}{2}$$ is true for the given value of \(n\) $$ n=5: \text { Show that } 1+2+3+4+5=\frac{5(5+1)}{2} $$
You select a family with three children. If \(M\) represents a male child and \(F\) a female child, the sample space of equally likely outcomes is \(\\{M M M, M M F, M F M, M F F, F M M FMF, FFM, FFF\)} - Find the probability of selecting a family with $$\text{at least one male child.}$$
Fifty people purchase raffle tickets. Three winning tickets are selected at random. If each prize is \(\$ 500,\) in how many different ways can the prizes be awarded?
Some three-digit numbers, such as 101 and \(313,\) read the same forward and backward. If you select a number from all threedigit numbers, find the probability that it will read the same forward and backward.
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