How many arrangements of letters in INSTRUCTOR have all of the following properties simultaneously? (i) The vowels appear in alphabetical order. (ii) At least two consonants between each vowel. (iii) Begin or end with the 2 Ts (the Ts are consecutive). everything must be met

Q: A manager wants to award prizes for 1", 2nd and 3rd to his team members according to number of new…

A: We have given that the team is formed of 25 members and the prizes be awarded.    Permutation…

Q: A class has 26 students. In how many different ways can five students form a group for an​…

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Q: A merchant surveyed 330 people to determine the way they learned about an upcoming sale. The survey…

A: Use the following formulae, to obtain the solution.…

Q: How many books must you choose from among a collection of 7 mathematics books. 18 books of short…

A: Given information  No of mathematics book = 7 No of short stories books = 18 No of chemistry books =…

Q: (a) In a certain state, license plates have two letters followed by four digits. How many such…

A: a) There are 26 letters (A-Z) and 10 digits (0-9) Numbers and letters can repeat. We can pick 2…

Q: In a group of 500 people, 350 speak Hindi and 300 speak English. It is given that each person speaks…

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Q: A company sells regular hamburgers as well as a larger burger. Either type can include cheese,…

A: Introduction: According to the combination rule, if r distinct items are to be chosen from n items…

Q: A manager wants to award prizes for 1st, 2nd and 3rd to his team members according to number of new…

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Q: 1. There are 6,800 people in town. Are there at least 6 people that share the same birthday? a. Let…

A: This problem is based on the Pigeonhole principle, so I used the formula of this Principle to solve…

Q: (a) In a certain state, license plates have two letters followed by three digits. How many such…

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Q: How many possible results are there that A finished the first, B finished the second, and C finished…

A: SIX STUDENTS ARE SELECTED TO RUN 100 METER SPRINT. ASSUME THAT THEY ARE EQUALLY GOOD AND RESULT ARE…

Q: In how many ways can you orient the letters in the word "APPLICATION" such that A's don't sit next…

A: consider in 'APPLICATION " two A's sit together . in 'APPLICATION " n(A)=2, n(P)=2 n(L)=1 n(I)=2…

Q: How many ways can the letters be arranged? If each letter is distinct (that is, each letter E is…

A: Consider the letters of the word ELEEMOSYNARY Total 12 letters E occurs 3 times Y occurs 2 times…

Q: a. A coin is tossed 3 times. Find out the number of outcomes. b. In how many ways can the letters of…

A: a) When tossed a coin 3 times then  then we have possible combinations of outcomes  are - { HHH,…

Q: (d) Given the word PERMISSION, in how many ways can all the letters be arranged if (i) Number of…

A: Solution

Q: A group of 10 friends go out for dinner at a fancy dining room andthey each leave their hat with an…

A: A group of 10 friends go out for dinner. 5 of the friends were  wearing fedorasand and the other 5…

Q: At the Athens House of Pizza the House Special is a pizza where the customer chooses the type of…

A: The objective is to find out number of different House special pizzas possible.

Q: Six people attend the theater together and sit in a row with exactly six seats. Suppose the group…

A: Given,no.of men =3no.of women=3total no.of people=6

Q: 5. a) How many ways can 6 people be lined up to get on a bus? b) If a certain 3 persons insist on…

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Q: Moe, Joe, and Hiram are brothers. One day, in some haste, they left home with each one wearing the…

A: It is given that each one of them (Joe, Moe and Hiram) wore the hat and scarf of one of the other.…

Q: (g) A company has two employees with 12 offices. How many ways are there to assign different offices…

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Q: (ii) exactly ten buses arrive from 5.00 pm to 6.30 pm, and three buses arrive from 6.30 pm to 7 pm?

A: please do (ii) only .   In one hour time, average number of buses leaving station A = 12  then , In…

Q: Students are building their schedules at a small university. There are 12 departments offering…

A: There are 12 departments offering classes. A students have to build a schedule of 5 courses each…

Q: 10. Suppose there are 10 women and 8 men who teach at a private school. Please simplify your answers…

A: a) There are two cases for the given situation. Case 1.  2 teachers are women and 1 is man. Case 2.…

Q: There are 10 guests (1 is the host) in a conference. In how many ways can he accommodate his guests…

A: total number of guest =10 number of ways  person can arrange in circular table is (n-1)!

Q: A mail man has special -delivery for 10 customers. (i) In how many ways can he deliver to all? ii)…

A: i) deliver to all means arranging 10 customers in  all ways possible Total number of ways = 10! =…

Q: Crisha has 5 different colored beads including purple and pink. In how many ways can she arrange the…

A: a). It is given that there are 5 different colored beads. Since there is no restriction on the…

Q: As a vacation souvenir, a family of 4 members wanted to be photographed together with their 2 pets…

A: A family of 4 members wanted to be photographed together with their 2 pets (a cat and a dog). Given,…

Q: Suppose we want to choose 5 objects, without replacement, from 8 distinct objects. (a) If the order…

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Q: 5. Four married couples have bought 8 seats in the same row for a concert. In how many. different…

A: a). The number of possible permutations of n object is n!. So, the number of permutation for 8…

Q: Suppose we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk,…

A: Given we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk, and…

Q: 3. How many different ways are there to choose 6 items from 10 distinct items if... a. .the order of…

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Q: This is a question in discrete math and requires us to find the actual number of ways for these…

A: Seven numbered red balls and three indistinguishable blue balls are to be placedin five labelled…

Q: A group of 10 friends go out for dinner at a fancy dining room and they each leave their hat with an…

A: Given: Total number of people is, N=10. Number of people wearing fedoras hat is, nf=5. Number of…

Q: A jar is to be filled with 100 jelly beans. There are five varieties of beans to choose from and we…

A: As per given by the question,  The total number of jelly beans that is filled in the jar is 100.…

Q: You have 8 pairs of socks of different colours in one of your drawers [a pair has both socks of the…

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Q: A teacher requires students’ ways can this to answer 5 out of 10 questions, without regard to order.…

A: Given: Number of questions (n) = 10 Number of questions to be answered (x) = 5

Q: There are 7 performers who will present their comedy acts this weekend at a comedy club. One of the…

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Q: (a) In a certain​ state, license plates have two letters followed by three digits. How many such…

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Q: How many possible ways can a housewife take to buy a book from a bookstore, then buy groceries from…

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Q: How many ways can 120 identical packages be loaded into 10 delivery trucks where some trucks may…

A: There are n identical packages that must be loaded into 10 trucks in such a way that there are no…

Q: There are four boys and four girls at a party. In how many ways can they be seated in a row if they…

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Q: A student is given a reading list of nine books from which he must select two for an outside reading…

A: Given Data: The total number of books is: n=9 The total number of selection is: x=2 Assuming all…

Q: How many ways are there to seat 7 people at a round table in the following two different situations?…

A: Given that Number of persons to sit at a round table = 7

Q: A television director has to schedule commercials during 6 time slots allocated to commercials…

A: Answer: Using the given data,

Q: In an encyclopedia of​ language, the author presents five sentences that make a reasonable paragraph…

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Q: There are 7 different roads between town A and town B, 4 different roads between town B and town C,…

A: There are 7 different roads between A and C, 4 different roads between B and C and 2 different roads…

Q: A certain restaurant prepared meals during the pandemic for the first-responders. If they prepared 5…

A: We will construct a linear equation according to the given conditions and will solve it. Given that…

Q: How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear…

A: To find number of ways are there to arrange the 26 letters of the alphabet so that no pair of vowels…

Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…