MATH 112
Discrete Mathematics
Homework 6 - Solution
December 7, 2015
1. Find the prime factorizations of:
a. 20!
b.
!"
!"
2. Approximately how many 150-digit integers are primes?
3. Is 782 1 divisible by 83? Why?
4. Show that: , 1 | ! 1 ! using
mathem

MATH 112
Discrete Mathematics
Homework 4
November 9, 2015
1. You are given a square S with a side length of Fib(n) and a rectangle R with
side lengths Fib(n-1) and Fib(n+1), where Fib(n) stands for the nth Fibonacci
number. Can you tell which one, S or R,

MATH 112
Discrete Mathematics
Homework 2
October 12, 2015
1. For which value of ,
has the largest value?
Sln: 100
2. What is the coefficient of in the expansion of ( ) ?
Sln:
25
12
212313
3. In how many ways you can distribute balls to boxes if each box

MATH 112
Discrete Mathematics
Homework 1
September 28, 2015
1. In how many ways may 3 officers (Pres.,V.P., Sec.) be picked from
a 12 member club, if two people, Ahmet and Hasan, wont serve
together?
Ans: 1260
2. How many ways to seat four boys and three

MATH 112
Discrete Mathematics
Homework 5
November 20, 2015
1. You are allowed to choose three fruits at a grocery store. They have only two
identical apples, three identical oranges, and a banana left. But there are plenty
of (as many as you want) plums.

MATH 112
Discrete Mathematics
Homework 3
October 19, 2015
1. Using mathematical induction, prove that:
1 2 + 2 2 + 3 2 + . + n 2 = n (n + 1) (2n + 1) / 6
for all positive integers n. You have to follow the steps below for your
proof:
Step 1: What is the B