Suppose P is the set of numbers that are divisible by 5 and Q is the set of numbers divisible by 10. Is P subset Q? is Q subset of P?

Q: In how many ways can the letters of the word “rhubarb” be arranged so that all of the vowels are…

A: Given that, The letters of the word “rhubarb” should be arranged such that all vowels are together.

Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters codes can be…

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Q: Suppose that the number of subsets with k elements, made out of a set of n elements is called by the…

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Q: A 3-digit code is to be made from the set of digits {4, 5, 6, 7, 8}. a. How many codes can be formed…

A: Given:

Q: How many permutations of the letters A, B, C, D, E, F, G are there in which the three letters ABC…

A: Given letters are : A, B, C, D, E, F, G. and it is given that three letters A, B and C appears…

Q: Use the Venn diagram pictured with A representing the people in an arts dass and B representing the…

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

Q: Suppose 15 cars start at a car race. In how many ways can the top 3 cars finish the​ race? The…

A: Permutations: The number of permutations of r items selected from n items is, Prn=n!n-r! In this…

Q: 16. How many 6-element subsets of A = {0,1,2,3,4,5,6,7,8,9} have exactly three even

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Q: In how many ways can you seat 12 people at two round tables with 6 places each? Think of possible…

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Q: In how many ways can the letters of the word 'RETAIL' be arranged in such a way that the vowels…

A: The objective is to find out in how many possible ways can the letters of the word 'RETAIL' be…

Q: Suppose S= {a,b,c,d,e,f,g}. How many different three element subsets of S are there? How many…

A: We are given that S= {a, b, c, d, e, f, g}. First, we need to find the number of subsets (different)…

Q: Suppose we randomly select a subset of integers from the set {1, 2, 3, . .., 60}. How large must the…

A: A subset is the set smaller that the set of which it is a part. A set can be divided into multiple…

Q: The number of possible permutations if r objects are taken from n items is nPr =________.

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Q: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

Q: It turns out that 8 is solitary. Does this tell you anything about the truth or falsity of the…

A: Given the statement, "For all natural numbers n, if n is prime, then n is solitary". Given an…

Q: How many subsets are there of the set N = {9}?

A: Given,          The set is N=9We know that,         The number of subsets of a given set is 2n ;…

Q: ifferent ways can the letters

A: To find :  To find different ways can the letters of the word 'JUDGE' be arranged such that the…

Q: Consider the set A = {2,3, 4, 5, 6, 7}. a) How many different 4 digit numbers can you make from the…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 1. How many ways are there to choose a dozen donuts from 18 varieties: a) if there are no two donuts…

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Q: 2) From a deck of 52 playing cards, 5 cards are to be drawn. How many sets of 5 cards are possible…

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Q: Give two reasons why the set of odd integers under addition is not agroup.

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Q: A) How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Note :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: How many different user ID's can be formed from the letters W, X, Y, Z if no repetition of letters…

A: question:

Q: (a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if…

A: The counting can be done in 2 different ways, i.e. in first case the 1st digit can be 3 and in the…

Q: Let A = ,2,3,45,6,73 How many subsets ot Contriin d) How many anly even numbers? subsets. ot A…

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Q: 1. How many ways are there to choose a dozen donuts from 18 varieties: a) if there are no…

A:

Q: From the letters {A, B, C, D, E, F. G}, how :many 3-distinct-letters codes can be (a) generated? (b)…

A: a) 7C3 distinct codes can be generated by {A,B,C,D,E,F,G} which is equal to 21

Q: 1)Use the pigeonhole principle to prove the following statement.    Given any seven integers, there…

A: Solution: Given seven integers and we have to prove out of those seven  4 integers for which the sum…

Q: Consider 4 digit numbers with each digit from the set {1,2,3,4,5,6,7,8,9} a) How many such numbers…

A: Solution

Q: In how many ways can 6 books be choosen from a group of nine? Your answer is: Calculator > Next…

A: Given Data: n=9 x=6

Q: Some nonempty set has 211, at most two-element subsets. how many elements does this set have?

A: The number of ways, to select r number of different objects, from n number of different objects, can…

Q: Let S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Suppose six integers are chosen from S. Must there be two…

A: Consider the following given set:S = {3,4,5,6,7,8,9,10,11,12}Suppose six integers are chosen from…

Q: How many 98-element subsets does [100] have? (Here [100] is the set consisting of the first 100…

A: Given: Let us consider n be the number of elements in the set and r be the elements-subsets. Then, n…

Q: 4.The set of integers from 1 to 10 that is divisible by 3.

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Q: Let B = {dog, house, cheese, book, car, phone, egg, square}. How many subsets does B have? How many…

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Q: (a) How many 4-permutations are there of a set of six objects? (b) How many 2-permutations are there…

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Q: (a) How many 4-permutations are there of a set of five objects? (b) How many 2-permutations are…

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Q: A computer programming team has 13 members. Suppose seven team members are women and six are men.…

A: Solution: From the given information, the programming team has 13 members. Among them 7 are women…

Q: 1. Find the number of permutations of the elements in the set 1,3,5,7,9,11. 2. How many different…

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Q: How many three-digit numbers can be constructed from the digits 0, 3, 4, 5, 6, 8, 9 if: a)…

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

Q: If k, n are postive integers, with k<n, how many subsets of [n] are also not subsets of [k]?

A: Given k and n are positive integers with k&lt;n

Q: Is {2,2}={2, {2} }? How many elements are in the set {a,a,a,a,a}? {x€N|xis greater than 10 and x…

A: First we have to check 2,2=2,2. Here in set 2,2 2 is the element but in 2,2 2 and 2 are the…

Q: In a standard deck of 52 cards how many ways are there to: a) Pick a face card and a number…

A: Please refer to the image below,

Q: Is the set of permutations P(X), commutative? Justify your answer

A: .

Q: Let S = {Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows,…

A: Solution: Given that S = (Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka…

Q: Jar A contains numbers that are less than 26 and evenly divisible by 2. Jar B contains numbers that…

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Q: Television and radio stations use four call letters starting with W or​ K, such as WXYZ or KRLD.…

A: the total number of alphabets between A to P is 16.

Q: 9. C is the set of colors in the Philippine flag. 10. E is the set of even prime numbers.

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Q: 3. How many three digit numbers can be formed from the set 0, 1, 2, 3 .........9 if repetitions are…

A: Here Given Digits  Total Number=10 Here we will use Combination Method for Counting..