Knowee
Questions
Features
Study Tools

Answer the questions below.(If necessary, consult a list of formulas.)(a) There are 15 European cities that Hong would eventually like to visit. On his next vacation, though, he only has time to visit 4 of the cities: one on Monday, one on Tuesday, one on Wednesday, and one on Thursday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.)(b) A certain committee consists of 16 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.

Question

Answer the questions below.(If necessary, consult a list of formulas.)(a) There are 15 European cities that Hong would eventually like to visit. On his next vacation, though, he only has time to visit 4 of the cities: one on Monday, one on Tuesday, one on Wednesday, and one on Thursday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.)(b) A certain committee consists of 16 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

(a) This is a permutation problem because the order in which Hong visits the cities matters. The formula for permutations is P(n, r) = n! / (n - r)!, where n is the total number of options, r is the number of options chosen, and "!" denotes factorial.

In this case, n = 15 (the total number of cities) and r = 4 (the number of cities Hong will visit). So, the number of different schedules Hong can have is P(15, 4) = 15! / (15 - 4)! = 151413*12 = 32760.

(b) This is also a permutation problem because the order in which the committee members are chosen for the different offices matters. In this case, n = 16 (the total number of committee members) and r = 4 (the number of offices to be filled). So, the number of ways the 4 offices can be filled is P(16, 4) = 16! / (16 - 4)! = 161514*13 = 43680.

This problem has been solved

Similar Questions

Answer the questions below.(If necessary, consult a list of formulas.)(a) There are 13 European cities that Tony would eventually like to visit. On his next vacation, though, he only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.)(b) A certain committee consists of 16 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.

There are 15 European cities that Brian would eventually like to visit. On his next vacation, though, he only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.)

(If necessary, consult a list of formulas.)(a) There are 12 European cities that Kira would eventually like to visit. On her next vacation, though, she only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. She is now trying to make a schedule of which city she'll visit on which day. How many different schedules are possible? (Assume that she will not visit a city more than once.)(b) 72 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed?

Select the correct answer There are Seven Committee in a college viz., Academic, Alumni, Business, Cultural, Hostel, Placement and Sports. The Academic Committee meets every second day, the Alumni Committee meets every third day, the Business Committee meets every fourth day, the Cultural Committee meets every fifth day and the Hostel Committee meets every sixth day, the Placement Committee meets every Eighth day and the Sports Committee meets every Tenth day. How many times all the Seventh Committee do meets on the same day within days? radio_button_unchecked 12 radio_button_unchecked 9 radio_button_unchecked 6 radio_button_unchecked 3

A medical representative plans to visit six doctors A, B, C, D, E and F — one doctor per day - during a week from Monday to Saturday.i. He visited D on the day just before the day he visited B.il. He visited C on Monday.ili. He did not visit F on either Tuesday or Saturday.iv. He visited A on the day before the day he visited E.v. He visited D on some day after he visited A.Which doctor did he visit on Saturday?Question 12Answera.Eb.Dc.Ad.B

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.