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slamgirl [31]
3 years ago
15

Find the number of distinguishable permutations of the letters in the word supercalifragilisticexpialidocious?

Mathematics
2 answers:
m_a_m_a [10]3 years ago
7 0
"supercalifragilisticexpialidocious" has 34 letters, with 10 letters that appear more than once. In all, there are 34! permutations if we consider each letter to be distinct from any other, even duplicate letters.

If we assume duplicate letters are indistinguishable, then we need to divide this total by the number of ways we can permute those duplicate letters. For instance, the binary string 101 has 3! possible permutations, but in each permutation, we can rearrange the 1s in 2! ways (e.g. 101* and 1*01).

So in the word "supercalifragilisticexpialidocious", we have:

2 copies each of e, o, p, r, u;
3 copies each of a, c, l, s;
7 copies of i;

which means we have a total of

\dfrac{34!}{(2!)^5(3!)^47!}=1,412,469,529,257,855,275,311,104,000,000

possible permutations if we consider any duplicate letters identical.

Kryger [21]3 years ago
6 0

Answer:

1,412,469,529,257,855,275,311

Step-by-step explanation:

Find the number of distinguishable permutations of the letters in the word supercalifragilisticexpialidocious?

supercalifragilisticexpialidocious is about 34 characters

some letters appear more than once

they are

 e, o, p, r, u; 2 copies

a, c, l, s;  3 copies

 i- 7 copies

The permutations will be then

(\frac{34!}{(2!)^5(3!)^4(7!)}

SO WE HAVE

1,412,469,529,257,855,275,311 ways are the number of ways we can arranged the word supercalifragilisticexpialidocious.

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3 years ago
Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at colleg
zhenek [66]

Answer:

96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018 is  [335.89 , 356.10].

Step-by-step explanation:

We are given that a group of researchers at the BYU Off-Campus Housing department want to estimate the mean monthly rent that unmarried BYU students paid during winter 2018.

During March 2018, they randomly sampled 314 BYU students and found that on average, students paid $346 for rent with a standard deviation of $86.

So, the pivotal quantity for 95% confidence interval for the average age is given by;

           P.Q. = \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, \bar X = average rent paid by 314 BYU students = $346

            s = sample standard deviation = $86

            n = sample of students = 314

            \mu = population mean monthly rent of all unmarried BYU students

So, 96% confidence interval for the population mean monthly rent, \mu is ;

P(-2.082 < t_3_1_3 < 2.082) = 0.96

P(-2.082 < \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } < 2.082) = 0.96

P( -2.082 \times {\frac{s}{\sqrt{n} } } < {\bar X - \mu} < 2.082 \times {\frac{s}{\sqrt{n} } } ) = 0.96

P( \bar X -2.082 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X +2.082 \times {\frac{s}{\sqrt{n} } } ) = 0.96

96% confidence interval for \mu = [ \bar X -2.082 \times {\frac{s}{\sqrt{n} } } , \bar X +2.082 \times {\frac{s}{\sqrt{n} } } ]

                                                = [ 346 -2.082 \times {\frac{86}{\sqrt{314} } } , 346 +2.082 \times {\frac{86}{\sqrt{314} } } ]

                                                = [335.89 , 356.10]

Therefore, 96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018 is [335.89 , 356.10].

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Answer:

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Step-by-step explanation:

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