Discrete Mathematics Answers

There are piles of identical red, blue, and green balls where each pile contains at least 10 balls.

(a) In how many ways can 10 balls be selected if exactly one red ball must be selected? (

(b) In how many ways can 10 balls be selected if at least one red ball, at least two blue balls, and at least three green balls must be selected? 

How many number of strings that can be formed by ordering the letters given:

(a) SCHOOL

(b) CLASSICS 

Suppose that a pizza parlor features four specialty pizzas and pizzas with three or fewer unique toppings (no choosing anchovies twice!) chosen from 17 available toppings. How many different pizzas are there?

At one point in the Illinois state lottery Lotto game, a person was required to choose six numbers (in any order) among 44 numbers. In how many ways can this be done?

In how many ways can we select a chairperson, vice- chairperson, and recorder from a group of 11 persons?

Two dice are rolled. How many outcomes give the sum of 7 or the sum of 11?

In how many ways can a string of length 5 be formed using the letters ABCDEFG without repetitions. It should begin with the letter F and end with the letter A. 

Let A= {1, 2, 3, 4}, and let R And S be the relations on A As follow: R = {(1,1),(1, 4),(3,2),(4,2),(4,3)} S = { (1,1),(1,2),(2,2),(3,3),(4,2),(4,4)) Then find out: 1. M𝑅𝑐 2. 𝑀𝑠̅ 3. M (𝑅∪ S)

Find these values ⌊−3.1⌋

b) Given

p="Front door is open

q="Back door is open"

r="Light is on"

s="The lift doors are open"

t="The lift is moving",

i)

write the following sentence in logic symbols: "When the front and back

doors are closed then the light is off"

write the following in words: SV (t As)

ii)