Review for Exam III MAT 112 Summer 2009
1. Find each number using the following Venn diagram.
U
A B
13 823
11
a. n(A)
b. n(B)
c. n(A0)
d. n(B0)
e. n(A∩B)
f. n(A∪B)
g. n(U)
2. Of the 500 incoming freshmen at a college, 100 speak German, 300 speak Spanish, and 50 speak both. How many speak
German or Spanish? How many speak neither?
3. A combination lock has five wheels, each labeled with the digits 0 to 9. How many lock combinations are possible?
4. A computer password consists of three letters. The first letter is one of U,V,W,X,Y, or Z, the second is one of A,B,C,
or D, and the third is one of M,N,O,P,Q,R, or S. How many different passwords are there?
5. From a standard 52-card deck, how many 7-card hands will have exactly 5 diamonds and 2 spades?
6. Evaluate 235!
231! .
7. How many nine-digit Social Security numbers have no repeated digits?
8. How many five-card hands from a standard 52-card deck will contain only threes and fives?
9. If a committee of 4 is chosen at random from a class of 30 students then what is the probability of choosing any particular
committee?
10. If a committee consisting of a president, vice president, treasurer, and secretary is chosen at random from a class of 30
students then what is the probability of choosing any particular committee?
