3.4 Additional Topics in Probability and Counting
A tourist in Ireland wants to visit six different cities. If the route is randomly selected, what is the probability that the tourist will visit the cities in alphabetical order? Round your answer to five decimal places.
0.00139
6^c 2/11^c 3
0.091
5^P 4/ 11^P 3
0.12
A delivery route must include stops at three cities. If the route is randomly selected, find the probability that the cities will be arranged in alphabetical order. Round your answer to five decimal places.
0.16667
The access code to a house's security system consists of eight digits. How many different codes are available if each digit can be repeated?
100,000,000
A delivery route must include stops at five cities. How many different routes are possible?
120
The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many different ways can a representative visit five of these to investigate this week?
15,120
10^c 4
210
10^P 5
30,240
6^P 4
360
Eight guests are invited for dinner. How many ways can they be seated at a dinner table if the table is straight with seats only on one side?
40,320
If a couple plans to have twelve children, how many gender sequences are possible?
4096
How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if A and B must sit together?
48
How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if C must sit to the right of but not necessarily next to B?
60
How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if D and E will not sit next to each other?
72
A tourist in Ireland wants to visit six different cities. How many different routes are possible?
720
If a couple has three boys and six girls, how many gender sequences are possible?
84
10^P 2
90
