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Contact [7]
3 years ago
11

Consider strings of length 10 which contain only letters from the set {A, E, I, O, U} and digits from {1, 3, 5, 7, 9}. Suppose r

epitition of letters is not allowed.
How many different strings are there?
How many different strings are there if the letters, i.e. A, E, I, O, U and the digits, i.e. 1,3, 5, 7, 9 must alternate?
How many different strings are there if all five letters must be adjacent in each string?
Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0

Answer:

a) There are 3,628,800 different strings.

b) There are 28,800 different strings if the letters ad digits must alternate.

c)There are 86,400 different string if all five letters must be adjacent in each string.

Step-by-step explanation:

There are 10 digits.

Our strings have the following format:

C1 - C2 - C3 - C4 - C5 - C6 - C7 - C8 - C9 - C10

repitition of letters is not allowed.

a) How many different strings are there?

C1 can be any of the 10, C2 can be 9, C3 can be 8, ...

So in total there are:

T = 10*9*8*7*6*5*4*3*2*1 = 3,628,800

There are 3,628,800 different strings.

b) How many different strings are there if the letters, i.e. A, E, I, O, U and the digits, i.e. 1,3, 5, 7, 9 must alternate?

There are the following possiblities:

5(l) - 5(d) - 4(l) - (4d) - ...

Or

5(d) - 5(l) - 4(d) - 4(l) - ...

So:

T = 2*(5*5*4*4*3*3*2*2*1*1) = 28,800

There are 28,800 different strings if the letters ad digits must alternate.

c) How many different strings are there if all five letters must be adjacent in each string?

L - L - L - L - L - D - D - D - D - D

D - L - L - L - L - L - D - D - D - D

D - D - L - L - L - L - L - D - D - D

D - D - D - L - L - L - L - L - D - D

D - D - D - D - L - L - L - L - L - D

D - D - D - D - D - L - L - L - L - L

There are T = 6*(5*5*4*4*3*3*2*2*1*1) = 86,400

There are 86,400 different string if all five letters must be adjacent in each string.

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Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not
Igoryamba

Answer:

Step-by-step explanation:

We would construct a confidence interval.

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

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The formula used is

Confidence interval =

Sample mean ± z × σ/√n

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