Using the digits 0 through 8, find the number of different 5-digit numbers such that: Digits can be used more than once. Digits cannot be repeated but can come in any order. Digits cannot be repeated and must be written in increasing order. Which of the above counting questions is a combination and which is a permutation? Explain why this makes sense.

Q: In a “Pick-4” game, a player wins a prize for matching a 4-digit number from 0000 to 9999 with the…

A: Given: A player wins a prize for matching a 4-digit number from 0000 to 9999 with the number…

Q: Solve each problem. Show your solution following the Fundamental Counting Principle. 1. How many…

A: As per the Bartleby guildlines we have to solve first question and rest can be reposted... Given…

Q: If n is a counting number, bn, read_______ ,indicates that there are n factors of b. The number b is…

A: bn reads b to the power n. b is called the base and n called the exponent.

Q: Q4 : Consider the 5 - digit numbers , with distinct digits ( no repetition ) , that can be formed…

A:

Q: Use the Fundamental Counting Principle to solve:A popular brand of pen is available in three colors…

A: Given, A pen available in three colors red, green , or blue and, four writing tips bold, medium,…

Q: Answer the following questions. Give justifications and explanations when needed. c) At an…

A:

Q: Toss 5 coins 20 times simultaneously and observe the number of heads that will occur. The possible…

A: Given:  There are 5 coins tossed 20 times simultaneously.  X = number of heads  X is a random…

Q: Under the standard rules for counting significant​ digits, which of the following numbers has the…

A:

Q: How many different 9-digit phone numbers do not contain the digit 9? Assume that any digit in the…

A: Given data÷ How many different 9-digit phone numbers do not contain the digit 9. Assume that any…

Q: A sales representative must visit nine cities. There are direct air connections between each of the…

A: We have to find correct answer for given data..

Q: How many numbers less than 100 can be formed using only even-numbered digits, and repetition of the…

A: Given that : How many numbers less than 100 can be formed using only even-numbered digits, and…

Q: Use the fundamental counting principle to solve parts​ (a) and​(b). ​(a) In a certain​ state,…

A: Using the fundamental counting principle, it can be written that if there is a sequence of…

Q: Determine whether the following are Mutually exclusive, Not mutually exclusive or cannot be…

A: 1) A person is watching TV and sleeping - Mutually exclusive 2) Getting a grade of 90 in Math and a…

Q: WRITE P IF PERMUTATION, WRITE C IF COMBINATION, WRITE FC IF FUNDAMENTAL COUNTING PRINCIPLE   1.…

A:

Q: 20 applicants from a pool of 90 applications will be hired. How many ways are there to select the…

A: There are total 90 applications and we have to select 20 applicants.   So we have to find the number…

Q: 5. Forming 3-digit numbers from the digits 1, 2, 3, 4, and 5, if repetition is allowed; if…

A: Given that there are 5 digits 1, 2, 3, 4, 5. And if repetition is allowed then forming the 3 digit…

Q: • Suppose repetitions are not permitted. (a) Find the number of three-digit numbers that can be…

A: There are several powerful methods for counting objects and sets of objects without actually having…

Q: Tickets are numbered from 1 to 25. 6 tickets are chosen. In how many ways can this be done if the…

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Q: How many permuations are possible without repeats for P(5,3) O 60 O 125

A:

Q: Suppose a marketing company did do a survey. They randomly surveyed 200 households and found that in…

A:

Q: How many different 7-digit phone numbers do not contain the digit 8? Assume that any digit in the…

A: we know that we have 10 digits 0,1,,2,3,,4,5,6,7,8,9 if we do not use digit 8 then we left with9…

Q: Three - digit numbers are formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. a.) How many…

A: Solution

Q: How many different 8-digit phone numbers do not contain the digit 9? Assume that any digit in the…

A: Please rate and feel free to ask any query about any part of the question.

Q: How many different 7-digit phone numbers do not contain the digit 88? Assume that any digit in the…

A: Note: Hi there! Thank you for posting the question. As some information in the question seems to be…

Q: Use the Fundamental Counting Principle to solve:The model of the car you are thinking of buying is…

A: The given situation involves making choices between two groups i.e., Total choices in colors: 9.…

Q: Use principles of counting for following problems How many ways are there to choose five donuts if…

A: 1).Given,            r=5,   n=8

Q: Counting numbers are to be formed using only the digits 6​, 7​, and 8. Determine the number of…

A: Given that: Counting numbers are to be formed using only the digits 6​, 7​, and 8. To find:…

Q: Q4: Consider the 6-digit numbers, with distinct digits (no repetition), that can be formed using the…

A:

Q: How many scrambles (re-arrangements of the letters) of the word samson are there? Give your answer…

A: If there are n elements, of which n1 are of type 1,  n2 are of type 2,  n3 are of type 3, and so on,…

Q: Determine P(even and multiple of 3) from a list of numbers 1 through 30

A: It is given that  There is  list of numbers 1 through 30 i.e. S={1,2,3,....,30} i.e. n(S) =30 Let us…

Q: Solve the problem by applying the Fundamental Counting Principle. Arestaurant offers a choice of 4…

A:

Q: Q10) In a grand prix race with 6 cars, how many different possibilities are there for the order of…

A:

Q: Use the Fundamental Counting Principle to solve:Six performers are to present their comedy acts on a…

A: Given: Six performers are to present their comedy acts on a weekend evening at a comedy club. One of…

Q: There are four wires which need to be attached to a circuit board. A robotic device will attach the…

A: If an event can occur in m different ways and if for each occurrence of the first event a second…

Q: For which values of n does n! have n or fewer digits

A: Solution is as follows

Q: Find the number of permutations. Twelve objects taken seven at a time There are permutations.

A:

Q: Using the digits 0 through 8, find the number of different 5-digit numbers such that: (ANSWER…

A: While selecting the cases if the order of the selection matters then it is considered as permutation…

Q: Five singers are to perform at a night club. One of the singers insists on being the last performer…

A: Given Five singers are perform at a night one singer is the last performer

Q: Find the number of permutations. 7 objects taken 4 at a time There are permutations.

A:

Q: Use the Fundamental Counting Principle to solve. An ice cream store sells 5 drinks, in 5 sizes, and…

A: Given data,No of drinks =5No of sizes =5No of flavours =3In how many ways can a customer order a…

Q: A state makes license plates with three letters followed by three numbers with no repetitions of the…

A: Permutation:It defines the number of possible ways an object can be arranged or ordered. The formula…

Q: 38) To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 55…

A: We have to find the number of selections possible.

Q: Solve the problem by applying the Fundamental Counting Principle with two groups of items. How many…

A: If the 1st letter must be S or T how many 4 letter codes can be formed?

Q: Using the digits​ 0, 1,​ 2, ...8,​ 9, determine how many 33​-digit numbers can be constructed…

A: Consider the provided question, The given digits are 0, 1, 2, 3,…, 8, 9. Determine how many 3 digits…

Q: Counting numbers are to be formed using only the digits two, six, seven, nine, one and eight…

A: We have to find number of two digits number posible

Q: Find the number of permutations. 10 objects taken 2 at a time There are permutations

A:

Q: Forming 3-digit numbers from the digits 1, 2, 3, 4, and 5, if repetition is allowed; if repetition…

A: Given that there are 5 numbers 1, 2, 3, 4, 5. And given that if repetition is allowed: Then the…

Q: There are six wires which need to be attached to a circuit board. A robotic device will attach the…

A: From the given information, Consider,  Total number of wires for attaching in a circuit board = 6…

Q: a.)Are possible in all, if repetitions are allowed? b.)Are possible in all, if repetitions of…

A: Use the given information to find different combinations.

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.