A bagel shop has bagels in the following six varieties: plain, sesame, onion, blueberry, asiago cheese, and everything. Assuming there are at least 20 bagels of each variety, how many ways are there to choose 20 bagels... a. with no restrictions. b. with three or fewer blueberry bagels. c. with three or fewer blueberry bagels and three or fewer onion bagels.

Three rooms in a university residence contain three beds, two beds, and five beds, respectively. In how many ways can ten students be assigned to these rooms?

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?

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?

Use Method of Laplace Transforms to solve each Initial Value Problems (IVP):

At a music​ festival, there are seven bands scheduled to​ play, numbered 1 through 7. a. How many different ways can these bands be arranged to​ perform? b. If band 2 is performing first and band 5 ​last, then how many ways can their appearances be​ scheduled?

What type of situation is the following? There are 6 youth basketball teams in the final round of a regional tournament. In the end, two teams will be selected to enter a national competition. How many ways are there to choose 2 teams out of 6 to enter the national competition? a) unordered b) ordered c) ranked

A class has 32 students. In how many different ways can four students form a group for an activity? (Assume the order of the students is not important.) C.. There are different ways that the four students can form a group for an activity. (Type a whole number.)

A Hawaiian favorite food is the "loco moco." It consists of a bed of rice under a meat patty with an egg on top smothered in brown gravy. The rice can be white or brown, the egg can be fried, scrambled, or poached, and the meat can be hamburger, Spam, Portuguese sausage, bacon, turkey, hot dog, salmon, or mahi. How many different loco mocos can be ordered?