Nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. In how many ways can this be done if Ben is to be in the picture? In how many ways can this be done if both Ed and Gail are in the picture? In how many ways can this be done if Dot is on the left end and Ed is on the right end

If a bag contains 4 blue marbles 6 red marbles and 9 green marbles then the number of ways that 3 marbles of the same color can be selected from the bag is : a.18 b. 969 c. 649 d.108

A large research project is looking for more researchers. There are 8 spots open on the research team. There are 10 mathematicians and 14 computer scientists that apply for the team. a. How many different ways can a team of 8 be made for the project? b. How many different ways can a team of 8 be made for the project if the team must contain at least one computer scientist and at least one mathematician.

On a business retreat, your company of 28 executives go golfing. a. You need to divide up into foursomes (groups of 4 people): a first foursome, a second foursome, and so on. How many ways can you do this? b. After all your hard work, you realize that in fact, you want each foursome to include one of the 7 Board members. How many ways can you do this?

Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket. When she gets home, she prepares her ingredients for lunch, but she forgets which of the tomatoes are cherry and which are grape. She cannot distinguish between the two types of tomatoes, so she just picks 13 tomatoes. How many different sets of 13 tomatoes are possible if there are exactly 7 cherry tomatoes?

A Horse Race has 12 horses.   How many different ways can the horses finish the race such that Grand Valor, Seabiscuit and Secretariat do not finish first?

there are 18 people from the mathematics department and 325 people from the computer science department in a collegea. how many ways are there to get two representatives?so that one person is from the mathematics department and the other is from the computer science department?b. how many ways are there to get one elected representative, from a combination of the two majors?

In how many ways can Mrs. Smith give a chocolate bar, a bag of potato chips, and a can of cane juice to 3 of the 21 students in her class, one item per student?

An ice cream store has 25 flavors to select from. A customer walks in and orders a three​-scoop ice cream cone. How many ways can the customer make this selection if... a. the flavors can be the same and the order is important​? b. the flavors are different and the order is not important​?