In the binary system, there are 2-digit numbers ranging from 10 (binary for 2) to 11 (binary for 3), which is 2 numbers. There are 3-digit numbers ranging from 100 (binary for 4) to 111 (binary for 7), which is 4 numbers. There are 4-digit numbers ranging from 1000 (binary for 8) to 1111 (binary for 15), which is 8 numbers. **

Yes, Amazon does require a three-digit PIN on the credit card when making certain transactions, such as adding a new card to your account or making changes to your payment methods. This additional security measure helps protect your account and prevent unauthorized use of your credit card information. It is important to keep your PIN secure and not share it with anyone to maintain the security of your Amazon account. **

There are 900 three-digit numbers that are representable. This is because a three-digit number can range from 100 to 999, inclusive. The total number of three-digit numbers can be calculated by subtracting the smallest three-digit number (100) from the largest three-digit number (999) and adding 1. **

Seven-digit prime numbers are prime numbers that have exactly seven digits. Some examples of seven-digit prime numbers include 1,000,003, 1,000,019, and 1,000,043. These numbers are only divisible by 1 and themselves, making them prime. There are infinitely many seven-digit prime numbers, but they become increasingly rare as the numbers get larger. **

To divide a four-digit number, you would use long division. First, you would divide the leftmost digit of the dividend by the divisor. Then, you would multiply the divisor by the quotient and subtract that from the current partial remainder. Bring down the next digit of the dividend and repeat the process until you have no more digits to bring down. This will give you the quotient and the remainder, if any. **

Yes, it is okay for your new credit card to have a 6-digit PIN. In fact, a longer PIN can provide an extra layer of security as it increases the number of possible combinations, making it harder for someone to guess or crack the code. As long as you can easily remember the 6-digit PIN, there should be no issue with using it for your credit card. Just be sure to keep it secure and not share it with anyone. **

There are 9 choices for the first digit (1-9), 9 choices for the second digit (0-9 excluding 0), and 8 choices for the third digit (0-9 excluding the two digits already chosen). Therefore, there are 9*9*8 = 648 three-digit numbers in which the digit zero does not appear. **

To find the number of nine-digit numbers that contain the digit 4 exactly three times, we can use the combination formula. There are 9 positions in a nine-digit number, and we need to choose 3 of them to place the digit 4. The remaining 6 positions can be filled with any of the remaining 9 digits (0-9) excluding 4. Therefore, the number of such nine-digit numbers is given by the combination formula: C(9,3) * 9^6 = 84,150. Therefore, there are 84,150 nine-digit numbers that contain the digit 4 exactly three times. **