Name: 

What is the value of 10!?

Solve for the variable:

An orchestra has 3 violinists, 5 cellists, and 3 harpists. Assume that the players of each instrument have to sit together, but they can sit in any position in their own group. In how many ways can the conductor seat the members of the orchestra in a line?

Solve for n in the expression .

Jenni and Hari go to a local Chinese restaurant for dim sum. If there are 18 items on the menu, and Jenni orders 6 items and Hari orders 10 items, which expression represents the total number of choices between them?

For which of the following terms is a = 66 in the expansion of (x + y)¹²?

Prom’s friend gives him a row of Pascal’s triangle and asks which row it comes from. Prom adds the numbers and obtains a sum of 2 097 152. Which row do the numbers come from?

How many terms are there in the expansion of ?

Which of the following has 9 terms in its binomial expansion?

A scout troop is arranged in a circle for an opening ceremony with its leaders. Assuming there are 10 troop leaders who stand together for the ceremony and 22 scouts in total, including the troop leaders, in how many unique ways can they be arranged around the circle?

Josie goes to the local submarine sandwich shop. She can choose from 21 types of sandwiches. There are 3 types of cheese, 8 types of vegetables, and 7 types of sauce. Assuming that Josie only chooses one type of cheese, one vegetable, and one sauce for her sandwich, how many choices does she have?

A math teacher is preparing a quiz for all of the students in grade 12. She wants to give each student the same questions, but have each student’s questions appear in a different order. If there are 128 students in the grade 12 class, what is the least number of questions the quiz must contain so everyone gets a test with the questions in a different order.

The chorus of a play has 17 females and 13 males. The director wishes to meet with 6 of them to discuss the upcoming production.
a) How many selections are possible?
b) How many selections are possible if the group consists of three females and three males?
c) One of the male students is named Ajay. How many six-member selections consisting of Ajay, two other males, and three females are possible?

Tanya goes to a fast food stand at the beach. There are 4 types of burgers, 3 sizes of French fries, and either orange pop or root beer to drink.
a) Create a tree diagram to show the possible choices of lunch if one of each item can be selected.
b) In how many ways can Tanya buy 2 burgers, 2 fries, and 2 drinks for her and her friend?
c) If Tanya does not like root beer and her friend does not like orange pop, how many possible choices are there?

On a Saturday, Charlie has to go to the library to study for a few hours, and then to the school to play a volleyball game.


a) How many routes are there for Charlie to go from home to the library if she only moves south and east?
b) How many routes are there for her to go from home to school moving only south and east?
c) Assuming Charlie moves south and east going from home to school and north and west going from school to home, how many routes are there for her to complete the round trip?
d) If Charlie could walk each route from home to school in 40 min, how long would it take her and her 22 classmates to walk all of the routes? Consider only the route from home to school, not the round trip.