**Problem Type 1:** An urn contains r red balls and b black balls. If k balls are chosen, what's the probability that t balls are red?

Download File: CombProb1 (.tex)

**Problem Type 2:** Enter a word in upper case, such as CALCULUS (shown above) and ask for the number of different arrangements of all the letters.

Download File: CombProb2 (.tex)

**Problem Type 3:** How many subsets are there of a given set? How many subsets have a particular size?

Download file: CombProb3 (.tex)

**Problem Type 4:** How many functions are there from an m element set to an n element set? How many of these functions are one-to-one?Download file: CombProb4 (.tex)

**Problem Type 5: (Inclusion-Exclusion)** How many numbers between 1 and N are divisible by primes $latex p_1,p_2,p_3$?

Download File: InclExcl (tex)

**Problem Type 6:** A committee will be made from 5 English teachers, 3 math teachers, and 4 history teachers. If the committee must have 2 teachers from different disciplines then how many committees are there?

Download File: Comb6 (tex)

**Problem Type 7:** How many nonnegative integers less than 100000

contain the digit 5?

Download File: Comb7 (tex)

**Problem Type 8:** A high school committee of 6 is to be made from 32 boys and 41 girls. Within this set of students there are 2 senior boys and 3 senior girls. How many committees of 3 boys and 3 girls are there that contain at least one senior boy and one senior girl?

Download File: Comb8 (tex)

**Problem Type 9:** Suppose the probability of having a girl is 1/3 and having a boy 2/3. Find the probability that a family of 5 has:

a) exactly 2 boys

b) at least 1 boy and 1 girl

Download File: Comb9 (.tex)

**Problem Type 10:** Suppose a system has 6 independent components, each of which is equally likely to work. Now suppose the system works if and only 5 components work. What is the probability the system works.Download File: Comb10 (.tex)

**Problem Type 11:** Find the value of C(9,6) and P(9,3). Show your steps.

Download File: Comb11 (.tex)

**Problem Type 12:** Find all the divisors of N.

Download file: DivisorsOfN (.tex)

**Problem Type 12:** Three darts are thrown at the dartboard. A score is given for each region where the dart lands and the total score is just the sum of the $3$ dart scores. Assume all three darts hit the dartboard. How many different total scores are there? Enumerate them with by drawing a tree diagram.

Download file: CombinDarts (.tex)

**Problem Type 13:** Imagine you have two 7-sided dice in which the sides of each die are equally likely to occur. Create a chart to show all possible outcomes and use it to find the

probability that the sum is prime.

Download File: ProbDice (.tex)

**Problem 14:** There are 3 problems built into this one, starting with the classic problem of the number of shortest paths in a grid, followed by the number of shortest paths that go through a particular point, followed by a probability calculation based on the 2 calculations.

Download File: CombGrid (.tex)