Critical Thinking You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friend tells you to use 5!. Who is correct? Explain.

Q: Fifty people purchase raffle tickets. Three winning tickets are selected at random. If first prize…

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Q: 4. In a Music club with 15 members, 7 people played piano, 6 people p 4 people did not play either…

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Q: A local brewey has 17 different beers on tap. How many ways can you order 6 pints? There are no…

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Q: ow many unique ways are there to arrange the letters in the word PRETTY?

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Q: How many ways you can draw 3 balls in a box of 5 balls, if we replace the ball in box after being…

A: Permutation: It means number of arrangements  be obtained  It is denoted by P(n,r) or Prn where n is…

Q: A person going to a party was asked to bring 3 different bags of chips. Going to the store, she…

A: Combination:   It is nothing but the objects are being selected when the order of selection is not…

Q: You draw one card from a standard deck of playing cards. If you pick a heart, you will win $10. If…

A: Given  Total number of cards=52 Number of hearts in a pack=13 Number of face card but not hearts=9

Q: Determine whether the statement, 'I used the permutations formula to determine the number of ways…

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Q: How many different ways can the letters of "kissing" be arranged? The number of different ways that…

A: We have given that a word ‘kissing’.

Q: Does the problem, 'A medical researcher needs 6 people to test the effectiveness of an experimental…

A: A medical researcher needs 6 people to test the effectiveness of an experimental drug and 13 people…

Q: 6. How many ways can you rearrange the word HOPE. (Use listing method)

A: As per the instruction, we will be answering the first one. For (6), Let us rearrange the word HOPE.…

Q: in when you use permutations to count things and when you use combinations to count things. Give an…

A: The selection of elements without arrangement can be represented by a combination of elements. In…

Q: Which word has the most permutations of its letters? abbas aabbcc books bikes

A: To select the word which has the most permutations of its letters. Word 'abbas' has five letters…

Q: Number of ways to select 4 video games out of 20 to pack for vacation. a. Permutations  b.…

A: From the given information we find the permutation and combination.

Q: n your English class, you are given a list of 12 books. You are to choose 3 books to read over the…

A: It is needed to select 3 books from the list of 12 books.

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

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Q: Determine whether the statement, 'I used the permutations formula to determine the number of ways…

A: The given statement is  'I used the permutations formula to determine the number of ways the manager…

Q: Decide whether you would use a permutation, a combination, or neither. Next, write the solution…

A: consider the given data on ice cream parlor has 32 different flavors. A super sundae allows a person…

Q: Licence plays in a particular state display 3 letters followed by 3 numbers. How many diffrent…

A: By using permutation and combination .

Q: How many permutations of the letters PRODUCT have consonants in the second and third positions?

A: There are total 400 permutations of the letters PRODUCT have consonants in the second and third…

Q: How many different ways can the letters of "jogging" be arranged? The number of different ways that…

A: The word “jogging” contains a total of 7 letters in which “g” letter is repeated 3 times.

Q: Find the number of different ways the letters of the word “BLUEBERRIES" can be arranged.

A: Given the word BLUEBERRIES Here B is repeated twice E is repeated thrice R is repeated twice and…

Q: Fifty people purchase raffle tickets. Three winning tickets are selected at random. If each prize is…

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Q: There are 6 books on a book shelf. In how many ways can you arrange the books on your shelf? Note:…

A: The number of books on a shelf = 6 There are 6 books can be arranged in 6 different places on a…

Q: Decide whether you would use a permutation, a combination, or neither. Next, write the solution…

A: By combination method:- nCr = n!/r!(n-r)!

Q: 8 Which word has the fewest permutations of its letters? A faster B census c follow D fierce

A: A) FASTER has all 6 distinct letters. So the number of permutation=6!=720B) CENSUS has 4 distinct…

Q: Baseball In the American Baseball League, a designatedhitter may be used. How many batting orders is…

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Q: Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The…

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Q: permutations а, { 16P3 } b { 9P4 } combinations а. { 9C5 } b. { 16C14 }

A: Find 16P3Solution:nPr=n!/(n-r)!  16P3=16!/(16-3)!  =16!/13!  =16⋅15⋅14⋅13!/13!  =16⋅15⋅14  =3360…

Q: Use the Multiplication Principle to find the total number of outcomes. 1. You are choosing a car.…

A: Let m choices to be made with n1 options for the 1st choice, n2 options for the 2nd choice, … , nm…

Q: 9. Ms. Gardner is thinking of a number The number is even It is not divisible by 3 It is not…

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Q: how many different meal sets can you place on your menu? b. What mathematical concepts did you use?…

A: Suppose you are preparing a menu that may be served in your newly built restaurant. If you have 3…

Q: Can you see ninths? How many spots in 7/9 of the set?

A: If we count all the spots, we get 18 spots. So the total number of spots is 18. 118(1 eighteenth) of…

Q: Survey Reliability A survey with 12 questions is designed so that 3 of the questions are identical…

A: Permutations Rule (with some identical items):

Q: ABCDEFGHIJKLMNOPQRSTUVWXYZ Consider the 26 'stick' letters as seen above: What is the most common…

A: There are two types of symmetry in a rosette pattern. Namely, cyclic symmetry and dihedral symmetry.…

Q: Can you see eighteenths? How many spots in 11/18 of the set?

A: Step:-1 Given that  In the given table there are 18 spots because each box of table contain one…

Q: 三 MULTIPLE CHOICE QUESTION How many ways are there to make 5- letter arrangements out-of the word…

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Q: Q2) Bill and Ted are planning trips to 9 countries this year. There are 13 countries they would like…

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Q: Find the number of distinguishable permutations of the letters in each word below. (a) initial (b)…

A: In this question, concept of permutation is used. Permutation Permutations are frequently confused…

Q: 2. Which word has the fewest permutations of its letters? а. Ice cream b. muffin С. cake d. pie

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: #16 What is the correct answer for 16?

A: Q-16) Option D is correct option.

Q: picture of a Venn diagram to represent the situation  Bowl A contains numbers that are less than 20…

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Q: Explain how you would know whether to use combinations or permutations. You can use examples to make…

A: There is a simple difference between the two.

Q: There are 9 books on a book shelf. In how many ways can you arrange the books on your shelf? Note:…

A: There are 9 books on a books shelf. That is, n=9

Q: How many ways can you rearrange the numbers 1, 2, 3, 4, 5, and 6? * Your answer

A: Given,1, 2, 3, 4, 5, 6,

Q: V. How many different ways can the letters of each word can be arranged?

A: HERE USE COUNTING PRINCIPLE

Q: 10. A researcher wants to learn what people at a shooting range think about gun safety. The…

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Q: Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The…

A: Combinations: It defines the number of possible ways an object can be selected from a group. In…

Q: Permutations & Combinations Use the following information to answer the next question In the first…

A: Here the team have played a total of  13 games out of which 9 they had won and the rest 4, they…

Q: Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The…

A: here combinations must be use. we are using combination because here order doesn't matter we have to…

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.