MATH HOMEWORK
1. (4pts each) What is
a. gcd(140,100)
b. lcm(140,100)
c. 13 mod 3
d. 26 mod13
e. 0 mod 8
2. (30pts) Prove that 
Please explain each step
fully.
3. (6pts) Assume there are 10 graduate students and 20
professors. The two groups
are disjoint.
How ways to
a. Staff a class with one professor and one grad student?
b. Staff a class with one instructor who is either a professor or grad student?
c. Staff the class with one professor and 3 grad students?
4. (9pts)What is the Pigeon Hole Principle? (Nothing complex please)
5. Persons A,B,C,D,E,F are to be seated in a row of six
chairs. How many ways are
there to
a. (5pts) seat them all?
b. (10pts )seat them if A and B must sit next to each other?
6. Given an 8 bit string.
a. How many way strings are there.
b. How many strings start with 11 or 00
c. How many strings start with 00 or ends with a 11.
