Of the 75 cars that Lindsay saw pass on the highway, 15% had an out-of-state license plate. How many had an out-of- state license plate?​

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.

Learn more about fractions here:

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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)