Each digit of a four-digit PIN can be any number from 0 to 9. What is the percentage of PINs with no digit repeated more than twice?
To find the percentage of PINs with no digit repeated more than twice, we need to determine the total number of valid PINs and then divide it by the total number of possible PINs.
Step 1: Calculate the total number of valid PINs.
Since each digit can be any number from 0 to 9, we have a total of 10 options for each digit.
First digit: We have 10 options (0-9).
Second digit: We have 10 options (0-9).
Third digit: We can have 10 options (0-9), but we need to exclude the two digits already chosen in the first two digits. Therefore, we have 10 - 2 = 8 options.
Fourth digit: We can have 10 options (0-9), but we need to exclude the three digits already chosen in the first three digits. Therefore, we have 10 - 3 = 7 options.
The total number of valid PINs is 10 * 10 * 8 * 7 = 5,600.
Step 2: Calculate the total number of possible PINs.
Each digit can be any number from 0 to 9. Therefore, we have a total of 10 options for each digit.
The total number of possible PINs is 10 * 10 * 10 * 10 = 10,000.
Step 3: Calculate the percentage of PINs with no digit repeated more than twice.
To calculate the percentage, we divide the total number of valid PINs by the total number of possible PINs and multiply the result by 100.
Percentage = (Valid PINs / Possible PINs) * 100
Percentage = (5,600 / 10,000) * 100
Percentage = 0.56 * 100
Percentage = 56%
Therefore, the percentage of PINs with no digit repeated more than twice is 56%.
Well, let's do some math! For the first digit, we have 10 options (0-9). For the second digit, since we are allowed to repeat, we also have 10 options. However, if we want to avoid repeating the first digit more than twice, we need to discount the option of choosing the first digit twice. So, for the second digit, we have 9 options.
Similarly, for the third digit, we have 8 options (as we can't repeat the first and second digits more than twice), and for the fourth digit, we have 7 options.
Thus, the total number of PINs with no digit repeated more than twice is 10 x 9 x 8 x 7 = 5,040.
Now, to calculate the percentage, we need to divide this number by the total number of possible PINs (10,000) and multiply by 100.
(5040 / 10000) x 100 ≈ 50.4%
So, approximately 50.4% of four-digit PINs have no digit repeated more than twice.
To find the percentage of PINs with no digit repeated more than twice, we need to determine the total number of possible PIN combinations and the number of PINs that meet the given condition.
First, let's calculate the total number of possible PIN combinations.
Since each digit can be any number from 0 to 9, there are 10 options for the first digit, 10 options for the second digit, 10 options for the third digit, and 10 options for the fourth digit. Therefore, the total number of possible PIN combinations is:
10 * 10 * 10 * 10 = 10,000
Now, let's calculate the number of PINs with no digit repeated more than twice.
To do this, we need to consider two cases:
Case 1: No digit is repeated at all. In this case, we have 10 options for the first digit, 9 options for the second digit (since it cannot be the same as the first digit), 8 options for the third digit (since it cannot be the same as the first or second digit), and 7 options for the fourth digit (since it cannot be the same as any of the previous digits). Therefore, the number of PINs with no digit repeated at all is:
10 * 9 * 8 * 7 = 5,040
Case 2: One digit is repeated twice, and the other two digits are different. In this case, we have 10 options for the repeated digit, 9 options for the first different digit, and 8 options for the second different digit. We also need to consider the different positions of the repeated digit, so we multiply by 4 to account for the four possible positions. Therefore, the number of PINs with one digit repeated twice and the other two digits different is:
10 * 9 * 8 * 4 = 2,880
Now, let's calculate the total number of PINs that meet the given condition:
5,040 + 2,880 = 7,920
Finally, we can calculate the percentage of PINs with no digit repeated more than twice:
(7,920 / 10,000) * 100 = 79.2%
Therefore, the percentage of PINs with no digit repeated more than twice is 79.2%.
In a four digit number, a digit repeated twice means 3 of the numbers are the same.
Repeated more than twice means repeated 3 times, or all four digits are the same.
PINs with no digit repeated more than twice would therefore mean pins which do not have identical digits.
Out of 10000 pins, there are only 10 PINs with identical digits, so the probability is
9990/10000.
Reduce the fraction for the proper answer.