Find the # of possible choices for a 2 digit password that is greater than 19. Then find the # of possible choices for a 4 digit PIN # if the digits can not be repeated. HELP!
160
To find the number of possible choices for a 2-digit password that is greater than 19, we need to determine the range of valid digits for each position.
1. The tens digit must be greater than 1. Hence, the options for tens digit are 2, 3, 4, 5, 6, 7, 8, and 9, making a total of 8 choices.
2. The units digit can be any digit from 0 to 9, so there are 10 choices for the units digit.
To find the total number of choices, we multiply the number of choices for each position: 8 choices for the tens digit multiplied by 10 choices for the units digit, which results in 80 possible choices for a 2-digit password that is greater than 19.
Now, let's move on to finding the number of possible choices for a 4-digit PIN number with non-repeated digits.
1. The first digit can be any digit from 1 to 9, so there are 9 choices.
2. After the first digit is chosen, the second digit can be any digit from 0 to 9, excluding the digit already chosen for the first position. This leaves us with 9 choices.
3. Similarly, after the first two digits are chosen, the third digit can be any digit from 0 to 9, excluding the digits already chosen for the first and second positions. This leaves us with 8 choices.
4. Finally, after the first three digits are chosen, the fourth digit can be any digit from 0 to 9, excluding the digits already chosen for the first, second, and third positions. This leaves us with 7 choices.
To find the total number of choices, we multiply the number of choices for each position: 9 choices for the first digit multiplied by 9 choices for the second digit multiplied by 8 choices for the third digit multiplied by 7 choices for the fourth digit. This gives us a total of 9 x 9 x 8 x 7 = 4,536 possible choices for a 4-digit PIN number with non-repeated digits.
To find the number of possible choices for a 2-digit password that is greater than 19, we need to determine the range of valid digits for each position of the password.
1. Determine the possible choices for the tens digit: Since the password needs to be greater than 19, the smallest possible value for the tens digit is 2, and the largest possible value is 9. So, there are 8 possible choices for the tens digit (from 2 to 9).
2. Determine the possible choices for the units digit: In this case, any digit from 0 to 9 can be used since there are no restrictions on the units digit. So, there are 10 possible choices for the units digit (from 0 to 9).
To calculate the total number of possible choices for the 2-digit password, we multiply the number of choices for each position:
Total number of choices = Number of choices for the tens digit × Number of choices for the units digit = 8 × 10 = 80.
Therefore, there are 80 possible choices for a 2-digit password that is greater than 19.
Now, let's move on to finding the number of possible choices for a 4-digit PIN number without repeated digits.
1. Determine the possible choices for the thousands digit: Since we cannot have repeated digits, the number of choices for the thousands digit is 9 (any digit from 1 to 9).
2. Determine the possible choices for the hundreds digit: Since we cannot have repeated digits, the number of choices for the hundreds digit is 9 (any digit from 0 to 9, excluding the digit already chosen for the thousands digit).
3. Determine the possible choices for the tens digit: The number of choices for the tens digit is 8 (any digit from 0 to 9, excluding the digits already chosen for the thousands and hundreds digits).
4. Determine the possible choices for the units digit: The number of choices for the units digit is 7 (any digit from 0 to 9, excluding the digits already chosen for the thousands, hundreds, and tens digits).
To calculate the total number of possible choices for the 4-digit PIN number, we multiply the number of choices for each position:
Total number of choices = Number of choices for the thousands digit × Number of choices for the hundreds digit × Number of choices for the tens digit × Number of choices for the units digit
= 9 × 9 × 8 × 7 = 4,536.
Therefore, there are 4,536 possible choices for a 4-digit PIN number without repeated digits.