Give the expansion of the binomial. Simplify your answer.

$$\left(1+\frac{x}{2}\right)^3$$

If A is any subset of a universal set U, complete the following.

a. $A \cup \phi=$ ?

b. $A \cap \phi=$ ?

c. $A \cup \bar{A}=$ ?

d. $A \cap \bar{A}=$ ?

e. $A \cup U=$ ?

f. $A \cap U=$ ?

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. $(20-1)^3$

Evaluate:

a. 2!

b. 3 !

c. 4 !

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?

Find the number of permutations of the letters.

MISSOURI

a. In how many ways can a club with 20 members choose a president and a vice president?

b. In how many ways can the club choose a 2-person governing council?

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

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 number of permutations of the letters.

a. MALE

b. MALL

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.

$$F \cap M$$

Draw a Venn diagram and shade the region representing the set given in part (a). Then draw a separate Venn diagram and shade the region representing the set given in part (b).

a. $P \cap Q$

b. $P \cup Q$

Find the value of expression.

a. ${ }_5 P_2$

b. ${ }_5 C_2$