Example 4 How many ways you can form a 5-digit number out of the following numbers: 0, 1, 2, 3, 5, 6, and 7, if repetition is allowed? Counting Principle Permutation Notation Answer

Q: DNA sequences have an alphabet {A,C,G,T}. How many DNA sequences of length n are there? (Two DNA…

A: given, DNA sequence have an alphabet { A,C,G,T } we have to find how many DNA sequence of length n…

Q: In how many distinct ways can the letters of the word MAMAS be arranged? ____ ways

A:

Q: How many ways can nine different books be arranged on a shelf? This type of problem is simply the…

A: There are 9 different books.we have to find the number of ways to arrange it on shelf.

Q: Subject identification numbers in a certain scientific research project consist of two digits…

A: Introduction: When there are some certain object and we have to arrange them or select them, we…

Q: Describe the difference between a permutation and a combination and give an example of each. Explain…

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Q: Example 1 In how many ways can the word "BOOK" be arranged

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Q: A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 13 choices for an…

A: Given: Number of choices for an appetizer =6 Number of choices for an entire =  13 Number of choices…

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: How many different​ three-digit numbers can be formed using the digits 3, 6, 1, 7, 8, 2, and 4…

A: How many different​ three-digit numbers can be formed using the digits 3, 6, 1, 7, 8, 2, and 4…

Q: EXAMPLE :- How many 3 digits number can be formed using digits 1,6,8,9,3,7 without repeating any…

A: Here use counting principle  Here total available digit 6

Q: How many five card hands at most three jacks are possible when dealt from a standard deck of 52…

A: No. of Jack Cards = 4 No. of non-jack cards = 52-4 = 48 No. of cards in hand  = 5

Q: If you are given the following table, which the most efficient counting method would you use to find…

A: Solution: Given output f(n) = 1, 4, 16, 64. The output sequence is of the form of geometric sequence…

Q: A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 11 choices for an…

A:

Q: A bookstore manager wants to select one novel from each category. There are 3 different fantasy…

A: Given that , A bookstore manager wants to select one novel from each category. There are 3 different…

Q: Example 5: How many different ways can the letters of the following words be arranged? a. QUEZON b.…

A: Arrangements of words: a). Given word is: QUEZON The letters of the following words be arranged:…

Q: Example 5 How many ways you can arrange the letters in the word SCRAPED, if the first letter is not…

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: Ехample 3 How many ways you can form a 4-digit number out of the following numbers: 1, 2, 3, 5, 6,…

A: Given digits are 1,2,3,5,6 and 7 We have to find how 4 digits are form

Q: How many three-letter permutations can be formed from the first nine letters of the alphabet?…

A: Given that  How many three-letter permutations can be formed from the first nine letters of the…

Q: Find the permutation. A picture is to be taken by lining up 5 of the 13 players of volleyball on…

A: Topic =  permutation

Q: Question: How many unique sequences of 3 symbols that can be formed from 9 symbols? Answer:…

A: Given that there are total number of 9 symbols. A unique sequence of three symbols have 2 or 3…

Q: Example 37. table so that no two ladies are together? In how many ways can 5 gentlemen and 3 ladies…

A:

Q: Example 57. How many of these will (a) Include one particular player In how many ways can a foot…

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Q: 6. For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to choose…

A: In this question, we have to choose 7 songs out of 13 songs, so number of arrangement is being…

Q: Birthday Problem In how many ways can 2 people eachhave different birthdays? Assume that there are…

A: Given; There are 2 people having different birthdays. To Find: In how many ways can 2 people each…

Q: Computer programming team has 13 members. A.) How many ways can a group of 5 can be chosen to work…

A: Given that Computer programming team has 13 members . We have to find the number of ways that  can a…

Q: 7. A jersey has 2-digit numbers. In how many ways can the number be arranged if (a) No double digit…

A: Given that a  jersey has 2-digit numbers. (a) The objective is to find the number of ways to arrange…

Q: A restaurant offers a $12 dinner special that has 7 choices for an appetizer, 13 choices for an…

A: Given values, Appetizers = 7Entree = 13Dessert = 3

Q: Example 38. 3 boys are together. In how many ways can 3 boys and 5 girls be arranged in a row so…

A: Given that  3 Boys and 5 Girls  We have to find  The number of ways can 3 boys and 5 Girls be…

Q: License plates in Edmonville consist of a digit other than 0 or 9, followed by any 2 letters, which…

A:

Q: Counting numbers are to be formed using only the digits 9,4,8,1 and 2. Determine the number of…

A:

Q: A four digit marathon race number is generated using only the digits 0, 1, 2, 3, 4, 5.  If…

A: We need four-digit race number and each place can be filled by 0, 1, 2, 3, 4, & 5

Q: 7. During the New Year celebration there are orange, purple, blue, and green fireworks. In how many…

A: Given Fireworks Colors = Orange , Purple, Blue and Green

Q: In how many different ways can a family of 4 sit around a table if they may sit in any way? Circular…

A:

Q: TOPIC: Permutation How many four-digit numbers can be formed from the digits 1, 2, 6, 8, 9 if: A.…

A:

Q: How many permutations are there of the following word? COMBINATORICS permutations

A: Given word is COMBINATORICS'c' is repeated 2 times'o' is repeated 2 times'I' is repeated 2 timesand…

Q: Answer permutation problem completely. Show complete solution. How many 4-digit numbers can be…

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Q: n how many unique ways can we rearrange the letters in the word COEFFICIENT?

A:

Q: (a) How many distinguishable permutations of the letters in the word “CORONA”?   (b) A bank has…

A: a) Given word is "CORONA" Number of letters = 6       (C , O, R, O , N, A) Letter O occurred twice.…

Q: How many ways can a deck of cards be drawn by shapes one by one up to the last card Note: There are…

A: Given: Number of cards =52 Objective is to find the number of ways can a deck of cards be drawn by…

Q: How many ways can one select a subset of 10 elements from {1, 2, 3, . . . , 1000} so that the…

A: We use the following summation: Crn+Cr-1=Crn+1nCmm+Cmm+!+Cmm+2+...+Cmn=…

Q: How many 5-digit numbers can be formed using the digits 2, 3, 4, 5, and 6 without repetition? With…

A: To find how many   5 digit number  can be formed using  2,3,4,5 and 6 without  repetition and then…

Q: umber of ways you can wear 10 outfits to school each day in a 5 day week. a. Combination b.…

A: Given data, Number of outfits n=10 Number of days in a week r=5

Q: using permutation or combination How many different license plates are possible if each plate…

A: Let us assume there are three final year students A, B and C sitting beside each other. The possible…

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: At Pizza Hut, the owner wants to display 6 different types of pizzas out of 11. How many different…

A: From the provided information, The owner wants to display 6 different types of pizzas out of 11. a)…

Q: How many four-letter sequences are possible that use the letters q, u, a, k, e, s at most once each?

A: Use permutation and combination