# In how many ways can the letters in the word MATHEMATICS be reshuffled so that all consonants appear together?

2 months ago

## Solution 1

Guest #2391178
2 months ago

75600

Step-by-step explanation:

We are given that  a word MATHEMATICS

Total letters =11

M repeated 2 times

T repeated 2 times

A repeated 2 times

Total vowels=4

Let MTHMTCS=P

Total number of ways in which MTHMTCS can be arranged=

PAEAI

Total number of ways in which PAEAI can arranged=

Total number of arrangements when all consonant appear together=

Total number of arrangements when all consonant appear together=

By using formula ;

## 📚 Related Questions

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You are given the following information: Stockholders' equity = $323 million; price/earnings ratio = 14; shares outstanding = 8,800,000; and market/book ratio =7.7. Calculate the market price of a share of the company's stock.. Solution 1 Answer:$282.59 per share

Step-by-step explanation:

Given that,

Stockholders' equity = $323 million price/earnings ratio = 14 shares outstanding = 8,800,000 Market/book ratio =7.7 Book Value per share: = Stockholders' equity ÷ shares outstanding =$323,000,000 ÷ 8,800,000

= $36.70 Market price per share: = Book Value per share × Market/book ratio =$36.70 × 7.7

= $282.59 per share Question The number of product units q assembled during one shift is a function of the number of employees, n. Suppose that this function is q=f(n)=60n−n3. The company profit p is a function of q, namely p=g(q)=43q−10000. Express the profit as a function of the number of employees n: Solution 1 Answer: 2580n -43n^3 - 10000 Step-by-step explanation: From the question: q= assembled product n = Number of employees q(f) = 60n - n^3 p=g(q)= 43q - 10000 P(q)= 43(60n - n^3) - 10000 P(q) = 2580n - 43n^3 - 10000 Question Gym A charges a new member fee of$65 and $20 per month Gym B charges a new member fee of$25 and $35 per month but you get a discount of 20% monthly Solution 1 Answer: it will take 5 months for both gyms to cost the same. Step-by-step explanation: Let x represent the number of months for which the total cost of gyms are the same. Gym A charges a new member fee of$65 and $20 per month. This means that the cost of using gym A for x months would be 20x + 65 Gym B charges a new member fee of$25 and \$35 per month but you get a discount of 20% monthly.

20% of 35 is 20/100 × 35 = 7

The monthly charge would be

35 - 7 = 28

This means that the cost of using gym A for x months would be

28x + 25

The number of months that it will take for the cost of both gyms to be the same would be

20x + 65 = 28x + 25

28x - 20x = 65 - 25

8x = 40

x = 40/8 = 5

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Greatest common factor of 6xy^2 and 8
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2

Step-by-step explanation:

6xy² = 1,2,3,6 ,x, y

8= 1,2,4,8

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What is minus 7 minus minus 9
Solution 1

Solution 2
-7 -  - 9.

- - =  +

-7 - (-9)

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Question
(a) calculate the value of the correlation coefficient between sale price and size. (give the answer to three decimal places.) r = .701 correct: your answer is correct. (b) calculate the value of the correlation coefficient between sale price and land-to-building ratio. (give the answer to three decimal places.) r = -.3462 incorrect: your answer is incorrect. (c) if you wanted to predict sale price and you could use either size or land-to-building ratio as the basis for making predictions, which would you use?
Solution 1

.701

Step-by-step explanation:

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Question
1 2 3 4 5 6 7 8 9 10 Time Remaining 59:45 Which statement best describes the use of a simulation to predict the probability that two randomly chosen people will both have their birthdays on a Monday? Randomly generate an integer from 1 to 2 seven times, and the probability is . Randomly generate an integer from 1 to 2 seven times, and the probability is . Randomly generate an integer from 1 to 7 two times, and the probability is . Randomly generate an integer from 1 to 7 two times, and the probability is . Mark this and return Save and Exit Next Submit
Solution 1

Option D is correct.

That is,

Randomly generate an integer from 1 to 7 two times, and the probability is (1/7) ^2

Step-by-step explanation:

The probability of having birthday on a particular day of a week for anyone is 1/7. That is, 1 day out of the 7 days in a week.

Then for another person to have birthday on that same day is mathematically given as

(1/7) × (1/7) = (1/7)²

And this corresponds to option D. Therefore option D is the statement that best describes the use of a simulation to predict the probability that two randomly chosen people will both have their birthdays on a Monday.

Hope this helps!

Question
If there were 5 million births in a particular country and 3 comma 375 sets of naturally occurring​ triplets, what is the experimental probability of having triplets​ naturally?
Solution 1

Step-by-step explanation:

The experimental probability can be defined as the ratio of the number of times any particular event has occurred to the total number of times that event has taken place.

Experimental probability = P = No. of event occurrences / total number of occurrences.

In our question statement,

No of naturally occurring triplets are = 3375

Total number of births = 5 million = 5,000,000

Putting values in equation.

Solution 2

Step-by-step explanation:

You just divide by 3,375/500,000 and get 6,75

Question
Three distinct integers are chosen at random from the first 20 positive integers. Compute the probability that: (a) their sum is even; (b) their product is even.
Solution 1

Step-by-step explanation:

There are first 20 positive integers 1,2...20. Three distinct integers are chosen at random.

Total no of ways of drawing 3 integers =

To  Compute the probability that: (a) their sum is even

a) Sum can be even if either all 3 are even or 1 is even and 2 are odd.

There are in total 10 odd and 10 even.

Ways of sum even =

Prob =

b) their product is even

Here any one should be even or both

SO no of ways are

=

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Question
Given a data​ set, how do you know whether to calculate sigma or​ s? Choose the correct answer below. A. If the given data set contains a large number of​ entries, then s is calculated. If the data set contains a small number of​ entries, then sigma is calculated. B. When given a data​ set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a​ population, then sigma is calculated. If the data are a​ sample, then s is calculated. C. When given a data​ set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a​ population, then s is calculated. If the data are a​ sample, then sigma is calculated. D. If the given data set contains a large number of​ entries, then sigma is calculated. If the data set contains a small number of​ entries, then s is calculated.
Solution 1

B

Step-by-step explanation:

S is the sample standard deviation, it is calculated when the observations represent a sample of the population. sigma is the population standard deviation, it is calculated when de observations are the whole population.

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