1. A multiset is a collection of objects, just like a set, but can contain an object more than once (the order of the elements still doesn't matter). For example, {1,1,2,5,5,7} {1,1,2,5,5,7} is a multiset of size 6. How many multisets of size 5 can be made using the 10 numeric digits 0 through 9?

Q: How would you write the set Q({∅,{∅,{∅}}}) in list notation?

A:

Q: how many different 5-digit codes can be formed if the first digit must be an odd number, the second…

A:

Q: List the elements of the set of all letters in the word ​'four'. The set of all letters in the word…

A:

Q: If A is the set of all whole numbers less than 20 that are divisible by, 4, and B is the set of all…

A: A∪B is the union of set A and set B. This set contains all the elements in set A or set B. The Venn…

Q: For some particular website, the password must start with one of the letters A, B, or C. Then there…

A:

Q: How many different passwords are possible? If a cell phone’s password consists of eight characters,…

A: Given that cell phone's password consists of eight characters. first character is 6. The number of…

Q: Suppose I had the set {1,2,3} and wanted to make a list of 5 of those elements that contained one…

A:

Q: Use the black and red chips model to describe three different sets, Set 1, Set 2, and Set 3, of…

A: Let black chips represent positive integers and red chips represent negative integers. Take the…

Q: Combinatorial questions: A bit have 2 states: 0 and 1. If bit could have 4 states (0, 1, 2, 3), how…

A: ans (d)  and (e)

Q: Any whole number is divisible by 3 if and only if the sum of its digits is divisible by 3 TRUE FALSE

A: We have to state that the given statement is true or false.   Any whole number is divisible by 3 if…

Q: For some particular website, the password must start with one of the letters W, X, Y, or Z. Then…

A: We have 10 digits and 26 alphabets in totalFor first letter we have 4 possible choices (W,X,Y, or…

Q: In how many ways can the world " mount " be arranged

A: The given word is ‘mount’.

Q: Find the number of subsets that can be formed from a set containing 10 elements.

A:

Q: How many computer passwords can be formed by rearranging the letters in the word "AARDVARCK’?

A:

Q: Let A = {1, 3, 5, 7, 9}, B = {3, 6, 9}, and C = {2, 4, 6, 8}. Find each of the following. (Express…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Assume that there are 55 students: 28 who enjoy tennis, and 14 who enjoy neither tennis nor…

A:

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: Let N= {1, 2, 3, 4, .} be the set of natural numbers and S= (1, 4, 9, 16, ...} be the set of squares…

A:

Q: How many different 3 letter codes can I make that do not contain any repeated letters

A:

Q: If the first even integer is 4, then what will be next three consecutive even integers ? O 5, 14, 10…

A: In the question it is asked to represent next three consecutive even integers after even integer 4.

Q: In a group of people, 68 people can speak English, 45 people can speak in Arabic and 19 people can…

A: It is given that 68 people can speak English, 45 people can speak Arabic and 19 people can speak…

Q: There are 40 cards in total. Every card has only one integer written on it. For each integer i = 1,…

A: The given data is as follows:20 cards are with number 0.Remaining 20 have numbers from 1 to 20

Q: Please answer all questions Question1: A password is a string of 8 characters taken from the…

A: GivenThe number of strings in a password =8 The number of alphabets =26The number of digits =10The…

Q: 1. How many 10-element multisets can be made from the symbols {1,2,3,4}?

A: Given Elements {1,2,3,4}

Q: Combinatorial questions: A bit have 2 states: 0 and 1. If bit could have 4 states (0, 1, 2, 3), how…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: How many different 2 letter passwords can be formed from the letters A, B, C, D, E, and F if no…

A:

Q: Suppose we have a set A={1, 2, 3, 4, 5, 6}. What is the partition of A into three parts? Make sure…

A: We can partition of set A as below

Q: A multiset is similar to a set, but can contain an element more than once. How many multisets can we…

A: You can identify every multiset with an ordered pair of usual sets, call them high and low. If you…

Q: Suppose that a password is exactly six characters and each character is 1 of the 26 lowercase…

A: The number of lowercase letters is 26 and the number of integers is 10.

Q: How many subsets are there of the set N = {5, 42}?

A: We ahave to find no. Of subsets.

Q: Each character in a password of length six can be any uppercase letter from A-Z or any symbol from…

A:

Q: Combinatorial questions: A bit have 2 states: 0 and 1. If bit could have 4 states (0, 1, 2, 3), how…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: How many 4-element subsets containing the letter A can be formed from the set {A, B, C, D, E, F, G}?

A:

Q: how many possible combinations are there for computer password that must contain six letters a…

A: Each of the places can take any letters from A to Z , as no repeat condition is given. Therefore,…

Q: A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A: From the given information, The universal set U with 66 elements has been partitioned into three…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.