Seven office mates, three women (Fran, Gladys and Helen) and four men (John, Karl, Leonard and Mark), eat only at restaurants A, B or C and there are the following restrictions:i.             Fran, the only day she eats at a restaurant is Wednesday and on the other days she eats at home.ii.            Gladys and Karl can never go to a restaurant together.iii.            Helen won't go to a restaurant unless Fran also goes.iv. John and Mark will not go to the same restaurant together unless Gladys also goes.v. Karl will never go to restaurant B.b. What is the maximum number of classmates who can go to eat together at one of the three restaurants on Tuesday (justify your answer)?i. 3ii. 4iii. 5iv. 6v. 7

Seven office mates, three women (Fran, Gladys and Helen) and four men (John, Karl, Leonard and Mark), eat only at restaurants A, B or C and there are the following restrictions:i.             Fran, the only day she eats at a restaurant is Wednesday and on the other days she eats at home.ii.            Gladys and Karl can never go to a restaurant together.iii.            Helen won't go to a restaurant unless Fran also goes.iv. John and Mark will not go to the same restaurant together unless Gladys also goes.v. Karl will never go to restaurant B.a.       If six of the classmates eat together at one of three restaurants on a Wednesday, which of the following will be absent (justify your answer)?i. Gladysii. Heleniii. Johniv. Karlv. Leonard

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.

There are 7 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last stand-up comic of the evening. If this performers request is granted, how many different ways are there to schedule the appearances?

There are four Olympians, Anne, Babaganoush, Carol, and David on the Canadian bobsledding team. As shown in the picture, all four members are needed to race at the same time. Only Babaganoush and Carol are qualified to be in the 1st position. Any member can fill the rest of the spots.   a.Determine the number of possible arrangements of the team

2.) The BOS-14 is the new model of cars manufactured by NUC Motors. This model can be achieved in 2 body styles, 4 interior options and 7 different colors. The model can be achieved in automatic transmission as a manual. ER Auto wants to have a model of each of the options available to sell. How many BOS-14 models should you order?

There are 53 students.  Of these, 25 are taking Business, 26 are taking English, and 25 are taking Math.  14 are taking both Business and Math, 13 are taking Math and English, and 17 are taking Business and English.  12 students are taking none of these three classes.  How many students are taking Business but are not taking Math?

If there are 11 employees in a club, in how many ways can they choose a dishwasher and a bouncer?

One pro basketball player was known for being a good shooter. In games during 1980-1982, when he missed his first free throw, 47 out of 54 times he made the second one, and when he made his first free throw, 248 out of 285 times he made the second one. Complete parts (a) through (c). a. Form a contingency table that cross tabulates the outcome of the first free throw (made or missed) in the rows and the outcome of the second free throw (made or missed) in the columns. 2nd free throw made 2nd free throw missed Total 1st free throw made 1st free throw missed Total b. For a given pair of free throws, estimate the probability that the player made the first free throw. (Hint: Use counts in the row margin.) The probability is (Round to the nearest hundredth as needed.) For a given pair of free throws, estimate the probability that the player made the second free throw. (Hint: Use counts in the column margin.) The probability is. (Round to the nearest hundredth as needed.) c. Estimate the…

1. A local restaurant serves tacos for $1 every Tuesday. For each taco, you must choose one filling, salsa, and tortilla. • Filling: Carne Asada, Pollo Asado, Al Pastor, Carnitas, Chorizo, Grilled Fish, Mushroom Salsa: Mild, Medium, Hot • Tortilla: Corn, Flour How many different kinds of tacos can be made?