Let U = the universal set of all teachers in your school. Let the subsets of mathematics teachers, biology teachers, physics teachers, and chemistry teachers be represented by M, B, P, and C, respectively. Describe in words the following set, and name a teacher belonging to each set if such a teacher exists in your school.

a. $\bar{M} \cap \bar{B} \cap \bar{P} \cap \bar{C}$

b. $\overline{M \cup B \cup P \cup C}$

Study Pascal's triangle. Describe the symmetry that the numbers in the triangle have.

Evaluate:

a. 2!

b. 3 !

c. 4 !

Evaluate:

a. 5!

b. 6 !

c. 7 !

d. 0 !

Give the expansion of the binomial. Simplify your answer.

a. $(a+b)^3$

b. $(20+1)^3$

c. $(20-1)^3$

Three identical door prizes are to be given to three lucky people in a crowd of 100. In how many ways can this be done?

Janet's payments on her 12,500 dollars car are 420 dollars a month for 3 years. Assuming that interest is compounded monthly, what interest rate is she paying on the car loan?

Of the 320 children at a movie, 190 buy popcorn and 245 buy something to drink. If 151 children buy both, how many buy neither?

Find the amount of an annuity that consists of 40 annual payments of $2000 each into an account that pays interest of 5% per year.

Find the amount of an annuity that consists of 24 monthly payments of $500 each into an account that pays 8% interest per year, compounded monthly.

Find the value of expression.

a. ${ }_5 P_2$

b. ${ }_5 C_2$

A certain small college has 1000 students. Let F= the set of college freshmen, and let M= the set of music majors. Describe the following set in words and tell how many members it has.

$$F \cap M$$

Find the number of permutations of the letters.

a. MALE

b. MALL

Find the number of permutations of the letters.

MISSOURI