Using the digits 0 through 8, find the number of different 5-digit numbers such that: (ANSWER SUBPART 4 ONLY) 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: Consider the 6-digit numbers, with distinct digits (no repetition), that can be formed using the…

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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: Use the fundamental counting pinciple. Gina must write evaluation reports on 2 hospitals and 3…

A:

Q: In a leap year there are 29 days in February instead of 28 days. That means there are 366 days in a…

A: Given in a Leap year there are 29 days in February instead of 28 days and the total days in a leap…

Q: How many arrangements are there of the letters of the word CHEESECAKE under each condition?…

A: According to the given word; Total number of C = 2 Total number of H = 1 Total number of E = 4 Total…

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

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Q: Solve each problem using the given techniques in counting. 1.) In how many ways can 5 people…

A: Note: As per bartleby guideline for more than one question only first is to be answered please…

Q: ich there are no repeated digits?

A: Available digits:   0,1,2,3,4,5,6,7,8,9 Total availeble position: 3 position   1st digit  2nd…

Q: a) Rowoon is trying to guess the COmbination to his combination lock. The "COmbination" is a…

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Q: if no repetitions are allowed, usinig the digits 0,1,2,3,4,5,6,7,8,9,  a. how many two-digit numbers…

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

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: How many four digits numbers can be made using 1, 2, 3, 4 and 0? Caution: your numbers cannot start…

A: 9

Q: Using the digits 1, 2, and 3, how many two-digit numbers can be formed if repetition is not allowed?…

A: Given: Available digits are 1,2,3

Q: Find the smallest positive integer N that satisfies all of the following conditions: • N is a…

A: We have to find the smallest positive. N'that satisfies all of the following conditions: N is 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: 15. Explain when to use a permutation and when to use a combination

A: Permutation is used for lists (order matters) and Combination for groups (order doesn't matter). A…

Q: . Determine whether the following are mutually exclusive, non-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: In a survey of 3303 adults aged 57 through 85 years, it was found that 84.8% of them used at least…

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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: Using the digits 0 through 8, find the number of different 5-digit numbers such that: Digits can be…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

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 2, 1, 4, 8, 9, 6, and 3. Determine the…

A: The objective is to determine the number of different possibilities for​ two-digit numbers which are…

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

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Q: Find the number of permutations of the letters in the word COEFFICIENT provided that all words start…

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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: Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder 1, 5 when…

A: To find- Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder…

Q: Using the set {1,3,4,6,7,8,9}, how many odd numbers can we construct between 100-999 if no element…

A: An odd number is determined by the unit digit. If the unit digit is an odd number, then the number…

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: How many positive integers greater than 5 and less than 2020 are divisible by 7? are divisible by…

A: 1) Here , 2020/7 = 288.57 So 288 multiples of 7 are there between 5 to 2020 So , 288 integers are…

Q: ario painted identification letters on his bicycles so that he could track which ones are being used…

A: Since every cycle is coded with three letters of English alphabets, which starts with alphabet M.…

Q: Using the digits 0 through 9, find out how many 4-digit numbers can be configured based on the…

A: The fundamental counting principle says that if there are n ways to choose something and m ways to…

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: A humane society claims that less than 72% of households in a certain country own a pet. In a random…

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Q: Two cards are drawn with the replacement from a standard deck of 52 playing cards find the following…

A: A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen…

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: 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: 2. Identify the pattern in the list of numbers. Then use this pattern to find the next number. 4, 8,…

A: In this question, we have to find out algorithm in pattern and solve for next number.

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: a) Using only the numbers 0, 1, 2, 5, 6, 7, and 8, determine how many 4 digit natural numbers are…

A: How many 4 digit natural numbers are possible using 0,1,2,5,6,7,8

Q: How many different 8-digit phone numbers do not contain the digit 6? Assume that any digit in the…

A: To determine how many different 8‐digit phone numbers do not contain the digit 6. Assume that any…

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.