90. Choosing a Delegation Three delegates are to be chosen from a group of four lawyers, a priest, and three professors. In how many ways can the delegation be chosen if it must include at least one professor?

5. Six friends, Brennan, Chad, Heather, Rona, Tracy and Trevor, are going to the theatre. The number of ways that they can sit in a row of six seats if Tracy and Rona do not sit next to each other is O 720 O 600 480 O 672

A club N with four members is shown below. N = {Aaron, Brad, Cindy, Dennis}, abbreviated as N = {A, B, C, D} Assuming all members of the club are eligible, but that no one can hold more than one office, list and count the different ways the club could elect both a president and a treasurer. Choose the correct list of possible pairs of presidents and treasurers. A. AA, BB, CC, DD B. AA, AB, AC, AD, BA, BB, BC, BD, CA, CB, CC, CD, DA, DB, DC, DD C. AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, DC D. AB, AC, AD, BC, BD, CD How many ways can a president and treasurer be elected?

4. In how many different ways can we select a committee consisting of 4 engineers 3 chemists, and 2 mathematicians from 7 engineers, 5 chemists, and 7 mathematicians?

3. A sports team has ten long distance runners, eight sprinters and five jumpers. A team of three long distance runners, five sprinters and two jumpers is to be selected. Find the number of ways of which the team can be selected ( 4. H

4. Six people attend the theater together and sit in a row with exactly six seats. a. How many ways can they be seated together in the row? b. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat? c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?

Seven people (A, B, C, D, E, F, G) are lining up to enter a museum. 1. How many ways are there to line up the seven people if B is somewhere before G, although not necessarily immediately before? 2. How many ways are there to line up the seven people if E, F and G are next to each other? 3. How many ways are there to line up the seven people if C must be next to E but D and F can not be next to each other? 4. How many ways are there to line up the seven people if C is next to E? 5. How many ways are there to line up the seven people if A must be somewhere before B, B must be somewhere before C, and C must be somewhere before D? (Note: some where before does not necessarily mean they must be next to each other)

A research team of 7 members must be formed from a group of 10 teachers consisting of 3 senior faculty, 4 junior faculty and 3 rookie faculty members. a. In how many ways can the selection be done if the team must include at least 1 senior faculty member? b. In how many ways can the selection be done if the team must include 2 seniors and at least 1 rookie faculty member?

a) Dave is choosing classes. He can choose from 4 different math classes, 3 different writing classes, and 7 different humanities classes. He needs to pick one of each of math, writing, and humanities. How many different schedules can Dave make? b) Dave goes to the squirrel farm to buy 6 squirrels. There are 19 different squirrels to pick from. How many ways can Dave choose the 6 he buys?

7. There are 7 boys and 5 girls in a class. а. How many ways can a committee of 4 people be selected if there must be 2 boys and 2 girls on the committee? b. How many ways can this committee of 4 people be selected if there must be at least 2 girls on the committee?