What fraction of all the 10-digit numbers with distinct digits have the property that the sum of every pair of neighboring digits is odd?

Answers

Answer 1

Answer:

The fraction of all the 10-digit numbers with distinct digits that have the property that the sum of every pair of neighboring digits is odd is 1/126.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

For a 10-digit number to have the property that the sum of every pair of neighboring digits is odd, the digits must alternate between odd and even numbers.

Specifically, if the firstdigit is odd, then the second digit must be even, the third digit must be odd, the fourth digit must be even, and so on.

If the firstdigit is even, then the second digit must be odd, the third digit must be even, the fourth digit must be odd, and so on.

There are 5 odd digits and 5 even digits, so there are 5 choices for the first digit. After selecting the first digit, there are 5 choices for the second digit (it must be one of the other type), 4 choices for the third digit (it must be the opposite type of the second digit), 4 choices for the fourth digit (it must be the opposite type of the third digit), and so on.

Therefore, the number of 10-digit numbers with distinct digits that have the given property is:

5 x 5 x 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 = 5! x 4!

where the factorials arise from the number of choices for each digit.

The totalnumber of 10-digit numbers with distinct digits is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!

Therefore, the fraction of all the 10-digit numbers with distinct digits that have the given property is:

(5! x 4!) / 10! = (5! x 4!) / (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 1/126

Thus,

The fraction of all the 10-digit numbers with distinct digits that have the property that the sum of every pair of neighboring digits is odd is 1/126.

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Answer 2

Answer:

Answer:

1/126

Step-by-step explanation:

Answer attached, I hope this is the answer.

the sum of every pair of neighboring digits is odd must be odd number and even number in the neighbor. (different parity)

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Answers

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If sin ⁡x=−1/2, and 270°* If 180°<θ<270°, and sin⁡θ=−3/4, what is the value of sin(−θ)?

Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

Dilation by a scale factor of 2 followed by a reflection over the y axis.

Step-by-step explanation:

The Y-axis is the vertical axis. So that cancels out the two about the x-axis. Then I counted the length of both triangles bases. Luckily for this one their bases aren't tilted but just flat. The big one is 6 and the small 3. Since it is going from one to the other you must find what number completes their equation. 3x = 6.

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If 4 gallons of milk cost $16.76, how much would 7 gallon of milk cost

Answers

7 gallons of milk will cost $29.33.

What is function?

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is that 4 gallons of milk cost $16.76.

Now, we can write that -

4 gallons of milk cost $16.76

1 gallon of milk will cost $(16.76/4)

7 gallons of milk will cost $(16.76/4 x 7) = $29.33

Therefore, 7 gallons of milk will cost $29.33.

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The answer is $29.33

What is the radius of a circle with circumstance of 22m

Answers

Circumference of a circle = 2πr = 22
2 * 22/7 * r = 22
r = 22 * 7 /44
r = 7/2

In short, Your Answer would be 7/2 m or 3.5 m

Hope this helps!

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