1.How many positive integers five-digit integers end with the digit 0? 9x10x10x10x? what number would represent zero

2.Using the digits {1,2,5,6,7,9} and not allowing repetition of digits, how many positive three-digit integers can be made that are larger than 500? 9x5x4
3.Assume that a license plate consists of 3 letters followed by 3 digits (the first of which cannot be 0). How many such license plates can be made? (dont know how)

1. To find the number of five-digit positive integers that end with the digit 0, you need to determine the possible values for the other four digits.

Since these integers are five-digit, the first digit cannot be zero, so we have 9 options (1-9) for the first digit. For the second, third, and fourth digits, we have 10 options (0-9) each. Finally, since we want the fifth digit to be 0, we have only one option for it.

So, the number of positive five-digit integers that end with the digit 0 is: 9 × 10 × 10 × 10 × 1 = 9,000.

2. To find the number of positive three-digit integers that are larger than 500 using the digits {1, 2, 5, 6, 7, 9} without repetition, we can break down the selection process.

For the first digit, we know it must be greater than 5. So we have 4 options {6, 7, 9}.

For the second and third digits, we can choose any of the remaining digits {1, 2, 5} since repetition is not allowed. So we have 3 options for the second digit and 2 options for the third digit.

Therefore, the total number of positive three-digit integers larger than 500 is: 4 × 3 × 2 = 24.

3. To find the number of license plates consisting of 3 letters followed by 3 digits (with the first digit not being 0), we need to consider the options for each part.

For the letters, we have 26 options for each of the three positions since there are 26 letters in the English alphabet.

For the digits, the first digit cannot be zero, so we have 9 options (1-9) for the first digit. For the second and third digits, we have 10 options (0-9) each.

Using the multiplication principle, we multiply the choices together to get the total number of possible license plates: 26 × 26 × 26 × 9 × 10 × 10 = 15,336,000.

Therefore, there are 15,336,000 possible license plates that can be made.

1. ok

2. ok
3. 26^3 * 9*10^2

for number 3 why do you times both?

think about it. For every combination of 3 letters (26^3), there are 900 ways to choose the following 3 digits.