How many arrangements are there of the letters of the word CHEESECAKE under each condition?                              When repetition is allowed? When arrangement starts with A? When the four E’s are to be together?

Q: How many permutations are possible with the letters TENNESSEE? If a student is to answer any 6…

A: Permutation is how many different ways are there for arranging n objects in r objects. where n>r…

Q: ) How many ways are there to select an unordered group of eight numbers between 1 and 25 inclusive…

A: a) The objective is to find that how many ways are there to select an unordered of eight number…

Q: For what values of nn will the number of ways of selecting nn items from 60 exceed the number of…

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Q: | st 5. There are 10 horses in a race. In how many ways can one pick the top three finishers (1st…

A: 3 horses can be selected out of 10 in 10C3=120 ways. Therefore one can pick top three finishers in…

Q: A 6-volume encyclopedia is to be placed on a shelf. How many incorrect arrangements are there?

A: Note- Since you have posted multiple questions, as per our guidelines we are supposed to answer only…

Q: In a group of 25 students, 15 are enrolled in Lab, 8 are enrolled in EconTwo, and 5 are neither…

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Q: A lock code requires 3 digits followed by 2 letter(s). How many different lock codes are possible?…

A:

Q: mbinations are possible? Assume the items are distinct. 7 ite

A: we need 7 items chosen 4 at a time therefore n = 7 x = 4

Q: Give a formula for the number of permutations of [n] with no cycles of length exactly 2. Your…

A: Formula for the number of permutations of [n] with no cycles of length exactly 2 is derived.

Q: Use permutations to solve. From a cooler with 6 different kinds of soda, 4 are selected for 4…

A: nPr = n!/(n-r)!

Q: How many days must be selected from the year to guarantee that at least 4 falls in the same…

A:

Q: How many 13-bit strings contain exactly six 1's?   (b) How many 13-bit strings contain at least…

A: a) If exactly 6 are 1's then (13-6)=7 will be 0's. When positions of 1's are fixed, then the…

Q: In a certain state license plates are formed by choosing 2 letters followed by 4 digits without…

A: Solution: Let L1 and L2 be the first two letters of a license plate.  For L1 we have 26 options…

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: A fair coin and 2 weighted coins with Pr[H]= 3/4 are in a bag. One is selected at random and then…

A: From the given information, A fair coin and 2 weighted coins are there in a bag. One is selected at…

Q: A club consists of 12 men and 15 women. In how many ways can this club choose a committee of 3 men…

A: We have given  A club consist of 12 men and 15 women We have to find in how many ways can this club…

Q: How many 12-bit strings contain exactly five 1's?   (b) How many 12-bit strings contain at least…

A: a) We can pick 5 positions for 1's from 12 positions in 12C5= 792 ways  Answer(a): 792

Q: A student is allowed to select at most n books from a collection of (2n+1) books. If the total…

A: We will solve the problem

Q: You brush your teeth very, very carefully in the morning at 6am leaving only 1000 bacteria on your…

A: We will find a sequence for number of bacteria .

Q: How many even 4-digit numbers can be formed from the digits 1, 2, 6, 7, and 9 with no repetitions…

A: There is no repetition allowed.. At unit place we have two choices 2 or 6 In 10th place we have…

Q: 4. How many 5 digit numbers can be formed if a) the digits 2-8 are available and there must be at…

A: 4. It is required to form 5 digit numbers under two different sets of conditions.

Q: Assuming that any arrangement of letters forms a 'word', how many 'words' of any length can be…

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Q: small combination on a suit case has 5 wheels, each labeld with 10 digits 0 to 9. How many 5 digit…

A: Given data, A small combination on a suit case has 5 wheels, each labeled with 10 digits 0 to 9.…

Q: Find the number of distinguishable permutations of: 6 Ds, 5 Js, and 2 Os

A: our objective is to find the no. of permutations

Q: If n = 3, what is 3n? Submit

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Q: A TV game show selects four contestants from an audience of 26 people. If the same 26 people showed…

A: Given: Total number of people=26Number of people selected=4 The permutation formula is applied when…

Q: How many times would you expect to roll a fair die before all 6 sides appeared at least once? (Hint:…

A: Consider Yi be the number of additional rolls required for a new side to appear until i-th side have…

Q: An object with negligible air resistance is dropped from the top of theWillis Tower in Chicago at a…

A: In this question we will use basic of algebra. We will simply write an expression of equations of…

Q: In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order…

A: Introduction: It is understood that a player wins the jackpot if they choose the 5 distinct number…

Q: How many arrangements can you make in a three letter word using the letters from the word "PINGUIN…

A: To find the number of three letters arrangement make from PINGUIN .

Q: 4. How many different arrangements are there of the letters in the word "success" and how many have…

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Q: How many combinations are possible? Assume the items are distinct. 19 items chosen 19 at a time…

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Q: 4. In some states,license plates consist of 3 letters followed by 2 or 3 digits (for example, JWK-…

A: Given: 4) License plates consist of 3 letters followed by 2 or three digits. To find: How many such…

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.

Q: Number of circular permutations of different .!things taken all at a time is (n-1)

A:

Q: How many different arrangements are there of the 8 letters in the word RELEASED in which the letters…

A: Here Given Word RELEASED So Here Number of letters in word=8

Q: How many permutations doesaa combination lock have if each combination has 3 numbers, no two numbers…

A: Permutation and combination : Permutation and combination are two distinct methods of representing a…

Q: 1. How many combinations are there to pick r objects from 2n objects numbered from 1 to 2n with n >…

A: For the solution of the problem follow the next step.

Q: How many different heptominoes (made from 7 squares) are there that have 5 squares in a column and 1…

A:

Q: . Find the number of permutations of the letters of the word ‘REMAINS’ such that the vowels always…

A: We can solve these questions using given details

Q: In how many ways can a person select seven party guests from 12 women  if he is to avoid having a…

A: Here we will use the concept of Combination

Q: How many permutations are there of the letters in the word 'CHARGES', if all the letters are used…

A: The formula for Permutation is nPr = n!/(n – r)!.

Q: 66. A has four shares in a lottery in which there are four prizes and five blanks. B has three…

A:

Q: Find the number of words, with or without meaning, that can be formed using the letters of the word…

A: We have to find the number of words, with or without meaning, that can be formed using the letters…

Q: 8. Find the number of different salads consisting of one or more of these vegetables – Tomatoes,…

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

Q: 1. This problem involves 8-digit binary strings such as 10011011 or 00001010. How many such strings…

A: Answer for sub question 1: The given task can be broken down into 8 sub tasks where the ith task Ti…

Q: In a certain state license plates are formed by choosing 2 letters followed by 4 digits where…

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Q: How many strings of four different hexadecimal digits are there?

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Q: A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second day, he…

A: Given - A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second…

Q: how many are the possible cases, regardless of

A: From the given information, The coin is tosses n times. And the coin has two faces.

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.