5. In how many ways can five dogs and seven cats be ordered in a row? (For example, "dccdcdcddcce" is one such ordering.) 6. A coin is tossed fiftoon times

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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5. In how many ways can five dogs and seven cats be ordered in a row? (For example, "dccdcdcddcce" is
one such ordering.)
6. A coin is tossed fifteen times.
a. How many sequences of heads and tails are possible? (e.g. "httttttthhhtht")
b. How many sequences are possible that result in a total of two heads? (e.g. "ttthtttthtttttt")
c. How many sequences are possible that result in a total of seven heads?
7. A die is rolled seven times.
a. How many sequences of results are possible? (e.g. "5211523")
b. How many sequences are possible that result in a total of six 3s? (e.g. "3333353")
c. How many sequences are possible that result in a total of three 5s and two 6s? (e.g. "5265561")
8. A fair coin is tossed ten times. What is the probability of obtaining the following outcomes?
# of heads:
probability:
10
9
8
7
9. A fair coin is tossed fifty times. What is the probability of obtaining...
a. fifty heads?
b. twenty-five heads?
6
5
10. There are twelve calico cats and seven tabby cats. In how many ways can the cats line up if no two
tabby cats can stand next to each other?
Transcribed Image Text:5. In how many ways can five dogs and seven cats be ordered in a row? (For example, "dccdcdcddcce" is one such ordering.) 6. A coin is tossed fifteen times. a. How many sequences of heads and tails are possible? (e.g. "httttttthhhtht") b. How many sequences are possible that result in a total of two heads? (e.g. "ttthtttthtttttt") c. How many sequences are possible that result in a total of seven heads? 7. A die is rolled seven times. a. How many sequences of results are possible? (e.g. "5211523") b. How many sequences are possible that result in a total of six 3s? (e.g. "3333353") c. How many sequences are possible that result in a total of three 5s and two 6s? (e.g. "5265561") 8. A fair coin is tossed ten times. What is the probability of obtaining the following outcomes? # of heads: probability: 10 9 8 7 9. A fair coin is tossed fifty times. What is the probability of obtaining... a. fifty heads? b. twenty-five heads? 6 5 10. There are twelve calico cats and seven tabby cats. In how many ways can the cats line up if no two tabby cats can stand next to each other?
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