How many ways can the letters of the word THEORY can be arranged in a row if TH must remain next each other as either TH or HT?     120       110       240     720

Q: QUESTION 14 If o =(1 3 4) in Ss then o=

A: The solution is given as

Q: Problem No.6: An airline association assigns three-letter codes to represent airport locations. For…

A: There are 26 letters in the English alphabet.

Q: Question 20 10101111 binary number is equivalent to which of the following decimal number 175 165…

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Q: Question 15 15) How many unique license plate numbers can be created made up of 3 letters (26…

A: The places of letters which are 26 possible can have the following pattern as they can be repeated:…

Q: QUESTION 4 Which is correct? 24 27 = 5 (mod 4) 72+5=32 (mod 9) 74 = 164 (mod 10) 19 x 27 = 7-3 (mod…

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Q: QUESTION 25 Use the Venn diagram below to find the number of elements 3 8. 15 10 n(AN C) O 10 O 18 O…

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Q: Nothing is known about the personal life of the ancient Greek mathematician Diophantus except for…

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Q: Question 5 Find all integers n >1 such that 1" + 27+...+(n – 1)" is divisible by n. |

A: To find all the integers n>1 such that 1n+2n+...+n-1n is divisible by n Proof: Let…

Q: QUESTION 9 If A =0 and B=1 then A NOR B is B 1 A

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Q: Find an explicit formula for an. 15) 0, -1, 0, 1, 0, -1, 0, 1, . . .

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Q: • Question 6 Suppose Set A contains 391 elements and Set B contains 421 elements. If Sets A and B…

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Q: Question 1 From the list below, choose the correct statements: O 17|0 5| 50 22| 11 O 4|(4n + 2)…

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Q: Question 6 (a) How many numbers with digits 1,2,3,4 of length 10 contain exactly six 3's? (b) How…

A: The digits used in making the number are 1, 2, 3, 4 and length of the number is 10. The combination…

Q: Question 3 Find all four-digit numbers abba with the property da - 106 = abba if a b.

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Q: Determine which of the following is the sum of the first forty terms of GP if first term is 40 and…

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Q: Rework problem 9 from section 2.2 of your text, involving the formation of a number from a list of…

A: Permutation and combination is used to calculate the number of possible ways to arrange or select a…

Q: Question 2  (a) A certain password consists of 6 digits. Find the number of possible ways this…

A: (a) Since the password cannot begin with the digit 7 so,  nine possibilities for the first digit…

Q: Question 9 How many ways can all the letters of the word MATHEMATICALLY be arranged? 87 178 291 200…

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Q: Question 11 Nancy read one third of a book, then she read one fourth of the remainder. If there are…

A: Let there are x pages in the book.  Nancy read one third of the  book means Nancy read (1/3)*x =…

Q: Question 20 1 pts ou have picked out 7 of your favorite CDs to play. How many different orders are…

A: We have to find permutations.

Q: Problem No.4: How many two-symbol code words can be formed if the first symbol is an uppercase…

A: The code has two- symbols.

Q: Question 8 The sequence a1 = 6, an = 3an-1 can also be written as %3D %3D A an = 6. 3" Can = 2.3" an…

A: a1=6,an=3an−1an=3an−1∴ a2=3⋅a1=3⋅6=32−1⋅6    a3=3⋅a2=3⋅3⋅6=32⋅6=33−1⋅6    a4=3⋅a3=3⋅32⋅6=33⋅6=34−1⋅6…

Q: QUESTION 12 The number of elements in S7 is 71 27 7!

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Q: Question 2 There are 101 houses on a street. Each house has an address between 1500 and 1699,…

A: This is a simple problem based on simple logic. Let us give a proper explanation to show that two…

Q: Question 10 How many three-digit odd numbers can be formed form the digits 0,1,2,3,4,5, and 6 if…

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Q: QUESTION 7 1 Let A = 7 and B 5 8 . Find (AB). 6 -5 -7 4 6 - 1 (AB)" 15 - 1 -44 36 (AB)" %3D 65 - 28…

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Q: QUESTION 12 The decimal representation of (142), is YOU MUST SHOW WORK FOR THIS QUESTION O 7910 O…

A: See the attachment. Answer is 79.

Q: Question 7 1 3 and A . 3 4 : If A = - KA – 512 = 0, then K =.. O 5 O 8 O 4 O 2

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Q: Problem 3: Let B, be the number of compositions of n in which the first part is odd. If n > 1, show…

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Q: Question 1 11:57:47 Explain is the statement sometimes, always, or never true. 1 If a > b, then a 1

A: Please refer to the image below.

Q: How many integers from 1 to 1000 are divisible by at least one of  the numbers 2, 3, 5?

A: Considering integers from 1 to 1000, Total integers  = 1000 Let n(A) represent the integers…

Q: Identify which of the following is the correct value of the number “m” for the hypothesis that “the…

A: Check for k=1 and k=2

Q: Rework problem 9 from section 2.2 of your text, involving the formation of a number from a list of…

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Q: QUESTION 16 Sum of two numbers is 67, and their difference is 29. Find the numbers. O 1.40 and 20…

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Q: 50 Question 8 Provide an appropriate response. How many distinguishable arrangements of all letters…

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Q: Nothing is known about the personal life of the ancient Greek mathematician Diophantus except for…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: QUESTION 2 Which is correct? 72+ 5 = 32 (mod 9) 74 = 164 (mod 10) 19× 27 = 7– 3 (mod 6) 24 – 27 = 5…

A: 72 + 5 = 49+5             = 54             = 9 (mod 9)             = 32 (mod 9) Hence 1 is true. 7 4…

Q: Question 8 (a) Use the pigeonhole principle to show that if you randomly arrange the numbers 1–12…

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Q: QUESTION 2 Let = {A, : nEN}, where A,=(0, - fe for each natural number n. Then N = N A, = Ø. n=1…

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Q: Question 26 1 2 4 6 is in NulA. 3 Let A =-1 1 -1 If | 0 1 1 then the value of a is and the value of…

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Q: QUESTION 4 Consider the equation x,+ +x,=35. How many different solutions does this equation have if…

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Q: Question 13 (Show your solutions) (a) How many four-digit numbers can be formed from the digit 0, 1,…

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Q: Question 3 (a) Given that the digit 7,8,9,10, and 11. How many four digits numbers: i. greater than…

A: (a) The given digits are 7, 8, 9, 10, and 11.

Q: Question # 01: Show how the following floating point arithmetic is performed: (Operations has to be…

A: (a_) Given- 0.7744×102+0.6666×101 To show- how the floating points arithmetic is performed. Concept…

Q: Question 1 Find all four-digit numbers abba with the property aa 10b= abba if a = b.

A: as given aa·10b=abba  claim- find all four digit numbers if a≠b

Q: QUESTION 1 Test the following number (83160) using the divisibility tests. Is this number divisible…

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Q: ACTIVITY 3- Solve the following problems on permutations. Write your complete solution in your…

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Q: Nothing is known about the personal life of the ancient Greek mathematician Diophantus except for…

A: Please refer the attached image for complete solution.

Q: Question 1 1.25 points Save Answer Ahmed must choose a seven-digit PIN number and each digit can be…

A: We have to find given no. Of possible ways to choose.

Q: Question 11 Write the number that corresponds to the correct answer. Conclude the test. 1. P-value…

A: A p-value is the probability value that represents the probability of the null hypothesis being…

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.