Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. (a) How many strings of hexadecimal digits consist of from one through three digits? The set of hexadecimal digits consisting of from one through three digits can be thought of as broken up into disjoint subsets: S,, S,, and so forth, where each S, consists of the strings with k hexadecimal digits. There are strings in S,, strings in S,, and so forth. Thus, by the ---Select--- v rule, the total number of strings is (b) How many strings of hexadecimal digits consist of from two through six digits?

Q: Assume that product codes are formed from the letters V, S, and Q, and consist of 4 not necessarily…

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Q: 7. How many positive integers between 100 and 999 inclusive are divisible by 78

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Q: How many strings of length two can be formed by using the letters A, B, C, D E and F without…

A: Given letters, A, B, C, D, E, F We have to find number of strings of length two

Q: let S = { 1,2,3,4,5,6,7,8,9,10,11,12,13}  HOW MANY SUBSETS ARE THERE TOTAL how many subsets have…

A: This is a counting problem.

Q: 1. How many 3 - digit numbers less than 150 can be formed from the digits 0, 3, 4, 6, and 9?

A: There are 5 digits that need to be used for required number formation. The number less than 150…

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

A:

Q: How many distinct scrambles (re-arrangements of the letters) of the word moximum. are there?

A: See the detailed solution below.

Q: Using the digitd 3, 4, 5, 6, 7, 8, and 9, how many 4-digit numbers can be constructed if the number…

A: Solution: From the given information, the digits are 3, 4, 5, 6, 7, 8 and 9. Here, the numbers with…

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: a) Count the number of distinct phone numbers, if a valid phone number must have the format…

A: To find-  Count the number of distinct phone numbers, if a valid phone number must have the format…

Q: The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is

A:

Q: In how many distinct ways can the letters of the word READERS be arranged? Oways

A: We have given that a word READERS. We need to tell the distinct number of ways of this word.

Q: Assume that product codes are formed from the letters A, B, C, D, and E, and consist of 5 not…

A: Product code is formed by the letters A, B, C, D, and E and consists of 5 not necessarily distinct…

Q: Assume that product codes are formed from the letters Q, X, W, T, S, Z, and Y, and consist of 6 not…

A: 1) There are total 7 letters, such that, Q, X, W, T, S, Z and Y.

Q: 3.55. a) How many three-digit numbers with different digits are there formed by digits belonging to…

A: As per the honor code, We’ll answer the first question since the exact one wasn’t specified. Please…

Q: Assume that you select digits from the set {2,3,5,7} to form a number between 20 and 700. (1) How…

A: The given set of digits is 2,3,5,7 and the range of numbers is 20 to 700. There would be 2 digit…

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly four 0s, four 1s,…

A: The 12 ternary digits can be arrange in 10! ways, in which exactly four 0s, four 1s, and four 2s can…

Q: A(n) _____ is a collection of items called elements

A:

Q: Assume that X={G,E,D,A}X={G,E,D,A} and Y={5,6,1,2,7}Y={5,6,1,2,7}. A code consists of 2 different…

A:

Q: How many positive integers between 100 and 999 inclusive   d) are not divisible by either 3 or 4?…

A: The set: A∪B contains all the elements that are present in set A or B. The set A-B contains all the…

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 numbers with nonrepeating digits from 4000 to 6000 can be produced using the…

A: The problem can be solved using the concept of permutation and combination.

Q: In a group of 200 college students, 138 are enrolledin a course in psychology, 115 are enrolled in a…

A: The Venn diagram:

Q: A multiset is a collection of objects, just like a set, but can contain an object more than once…

A: Q

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…

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Q: 22. Each symbol in the Braille code is represented by a rectangular arrangement of six dots, each of…

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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.) Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8,…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

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: how many subsetsof one or more elemets can be formed from a set containing 12 elements?

A: Use concept of power set

Q: Assume that product codes are formed from the letters T, Z, Q, V, Y, U, and X, and consist of 6 not…

A: To determine the total number of product codes satisfying different specified conditions

Q: In how many ways can the alphabet in the word "ILOVESTATISTICS" be arranged if the letter S must be…

A: Given word is  "ILOVESTATISTICS"Total no.of letters in the given word =15Letter "S" must be seated…

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: How many different number plates for cars can be made if each number plate contains four of the…

A: GivenEach number plate contains four digitsNo.of numbers from 0-8 = 8No.of letters from A-J = 10

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

A:

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly hree Os, five 1s,…

A: Strings of 12 ternary digits, 3 possibilities for each digit in the string, gives a total of 3^12 =…

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

A:

Q: Which of the following consists of 6 consec- utive composite numbers 2,3,5,7,9,11 7071, 7072, 7073,…

A:

Q: 25) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if…

A: This question is taken from the permutation and combination since the question is multiple hence we…

Q: How many four​-digit numbers may be formed using elements from the set {1, 2, 3, 4, 5, 6, 7} if no…

A:

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

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

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: Here are three boxplots on an unlabeled number line. A в Which boxplot has the following five-number…

A: It is a graph that shows five-number summary. The general boxplot is shown below:

Q: how many distinct proper subsets are in N={10,49,70,19,37,56,26}

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Q: How many integers from 1 to 500 are divisible by at least one of  the numbers 3, 4, 5?

A: Given :  Integers from 1 to 500 Total numbers  = 500 So to calculate the number of divisors, we will…

Q: How many three-digit numbers can be constructed from the digits 0, 1,2,3,4,5,6,8,9 if the number…

A: Given digits is0, 1, 2, 3, 4, 5, 6, 7, 8, 9Total no.of digits=10

Q: 11 How many 6-letter words (even without meaning) can be created from the letters of the word…

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Q: How many length-4 lists can be made from the symbols A, B, C, D, E that contains at least one letter…

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Q: Consider strings of lowercase letters. How many strings are there of lowercase letters of length…

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.