Shannon was born on 04/02/2004. How many eight-digit codes could she make using the digits in her birthday?

Answers

Answer 1

Answer: 420 different codes.

Step-by-step explanation:

We have eight digits, {0, 0, 0, 0, 2, 2, 4, 4}

For the first digit of the code, we will have 8 options.

For the second we will have 7 options (because we already took one)

for the third one we will have 6 options, and so on.

for the fourth, we will have 5 options

for the fifth, there are 4 options.

for the sixth, there are 3 options.

for the seventh, there are 2 options.

And for the last, there is only one option.

The total number of combinations will be equal to the product between the numbers of options for each digit, then we will have:

C = 8*7*6*5*4*3*2*1

But there is something more, the zeros can permute and will give the same code (So we are counting the same code several times), we have 4 zeros, then the number of permutations of the zeros is:

4*3*2*1  = 24

the 4's also are repeated, two times in this case, the number of permutations is:

2*1 = 2

And the 2's also are repeated, also two times, the number of permutations is:

2*1 = 2

Because we do not want to count these repetitions, we need to divide the total number of combinations by these 3 numbers of permutations

This means that we need to divide the number of different combinations will be:

c = (8*7*6*5*4*3*2*1)/(24*2*2) = 420

So we can conclude that there are 420 different codes.

Answer 2

The number of eight digit codes she can make using the digits in her birthday is; 420 eight digit codes

The 8 digits code of her birth date are;

0, 4, 0, 2, 2, 0, 0, 4

Now, since there are 8 digits, then number of ways of arranging the 8 digits is 8!

Since there are some repetitions, then we have to consider the permutations for them too.

There are four 0's which is 4!

There are two 2's which is 2!

There are two 4's which is 2!

Thus, number of 8 digit codes she can make using the digits on her birthday is;

8!/(4! × 2! × 2!) = 420 eight digit codes

Read more about permutations and combinations at; https://brainly.com/question/15301090


Related Questions

If -1 2/3 is subtracted from 5 1/2, what will be the result?

a. negative
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Answers

C    

Step-by-step explanation:

Answer:

B

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When subtracting a negitive number from a positive number the difference ends up being a positive. The answer is 7, therefore, greater than 4.

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Standard form

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Answers

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Answers

Answer:

The height of the flagpole is 46 feet

Step-by-step explanation:

First we find the ratio to connect the variables

Tan(∅) = opposite/adjacent

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Answers

Answer:

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Step-by-step explanation:

At a local high school, 40% of the students drink soda regularly, 30% of the students drink coffee regularly, and 10% of the students drink both regularly. If a
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Answers

Answer:

c he is your answer dear friend‍♀️‍♀️

Probability that the student drinks soda or coffee regularly is 60%

Option D is correct

Percentage of students that drink soda regularly, P(s) = 40%

Percentage of the students that drink coffee regularly, P(c) = 30%

Percentage of students that drink both coffee and soda regularly,

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Percentage of students that drink coffee or soda regularly is:

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P(s or c) = 40  +  30 - 10

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Probability that the student drinks soda or coffee regularly is 60%

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Hope this helps :) Have a great day!!!!

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:


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Answers

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Answers

Using the Pythagorean Theorem, we can determine that the length of CD is 11.62, rounded to the closest hundredth.

How Should One Put the Pythagorean Theorem Into Practice?

When the length of the longest side of a right triangle is squared, the result will be equal to the total of the squares of the lengths of the other two sides of the right triangle that are smaller.

Taking into account the following:

Side AB = 6

Side AC = 12

The perpendicular bisector theory states that AD equals half of AB, which equals half of (6), which equals three.

By using the Pythagorean theorem, we get the following:

The length of the CD is equal to (AC2 - AD2)

The length of the CD is equal to 122 minus 32.

The length of the CD equals (144 - 9)

11.62 is the length of the CD.

Consequently, by using the Pythagorean Theorem, we can determine that the length of the CD is 11.62, rounded to the closest hundredth.

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Which transformations could have occurred to map ABC to A"B"C?

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Answer:

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Step-by-step explanation:

Answer:

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Answer:

J

Step-by-step explanation:

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Answers

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What would this question look like after we change the mixed number to improper & use KCF to rewrite the question?
h) 3 1/2 divided by 1/3 =
A) 7/2 x 1/3
B) 7/2 x 3/1
C) 6/2 x 1/3
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Answers

Answer:

The question [tex]3\frac{1}{2}\div\frac{1}{3}[/tex] after change the mixed number to improper & using KCF will become : [tex]\mathbf{=\frac{7}{2}\times \frac{3}{1}}[/tex]

Option B is correct option.

Step-by-step explanation:

We need to change the mixed number to improper & use KCF to rewrite the question.

The expression is: [tex]3\frac{1}{2}\div\frac{1}{3}[/tex]

First converting mixed fraction into improper fraction

Multiply whole number with the denominator i,e (3*2=6) now add the numerator i.e (6+1) = 7/2

Solving:

[tex]3\frac{1}{2}\div\frac{1}{3}\\=\frac{7}{2}\div\frac{1}{3}[/tex]

Using KCF

KCF stands fro Keep it, Change it, Flip it.

It is used when division sign is converted to multiplication the term (1/3) is reversed to (3/1)

So, our expression will be

[tex]=\frac{7}{2}\times \frac{3}{1}[/tex]

So, The question [tex]3\frac{1}{2}\div\frac{1}{3}[/tex] after change the mixed number to improper & using KCF will become : [tex]\mathbf{=\frac{7}{2}\times \frac{3}{1}}[/tex]

Option B is correct option.

Two spoiled dogs eat a total of 18 treats in a certain amount of time. How many spoiled dogs will eat 72 treats in the same amount of time, assuming each dog eats treats at the same time

Answers

Answer:

8 spoiled dogs can eat 72 treats

Step-by-step explanation:

Answer:

8 spoiled dogs

Step-by-step explanation:

2 spoiled dogs = 18 eaten treats

18 eaten treats x 4 =72 eaten treats

2 spoiled dogs x 4 = 8 spoiled dogs

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Answers

Answer:

2 sorry if it’s wrong hope it helped

Step-by-step explanation:

What is mS?
R
Q
1000
s
T

Answers

Answer:

m<S = 80°

Step-by-step explanation:

The figure given shows a cyclic quadrilateral.

Angle S and Angle Q are opposite angles of the cyclic quadrilateral. Thus, it is known that opposite angles of a cyclic quadrilateral are supplementary. Since m<Q = 100°

Therefore:

m<S = 180° - 100°

m<S = 80°

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