Discrete Mathematics Answers

Write the set M = {1/3, 1/2, 3/5, 2/3, 5/7 ........} In the set builder form.

A panel is conducting an interview on six candidates of different heights. If they are to put them in line, in how many ways can they arrange them in line such that no three consecutive candidates are in increasing order of height from front to back?

1. If a quiz contains five multiple-choice questions, each of which has 4 choices. In how many ways can this be answered?
2. How many different ways can a visiting nurse see six patients if she is to visit at most 3 of them in one day?
3. How many different signals using 9 flags can be made if 4 are red, 3 are blue and 2 are white?
4. In how many ways can 5 individuals be seated in a round table with 5 chairs if 2 of them refuse to sit next to each other?
5. If a basketball team has 10 games to play, how many different outcomes of 6 wins and 4 losses are possible?
6.There are 12 people at a party. If they all shake hands once, how many different handshakes are there?
7. In how many ways can 6 individuals be seated in a row if three insist on sitting next to each other?

Draw both the NAND and NOR implementations of the below functions.

1) F(x,y,z)= x’y’ + xz’ + yz

2) G(x,y,z) = (x’+ y) (x + z) (y’+ z)

A panel is conducting an interview on six candidates of different heights. If they are to put them in line, in how many ways can they arrange them in line such that no three consecutive candidates are in increasing order of height from front to back?

Determine the number of positive integers x, where x <100 and x is divisible by 2,3 or 5

how many integers between 1 and 99 inclusive are divisible by either 2 or 3 or both

out of 50 students 30 are studying BASIC 23 are studying PASCAL and 10 both how many students study either language

prove that 1^2+2^2+3^2+-----n^2=n(n+1)(2n+1) for all positive integers

For the following decimal numbers, determine its binary representation. (Show full working)

a. 200
b. 300
c. 85
d. 77