what is the probability of getting two sets of 8 digit numbers having 5 digit are the same number and order.
To calculate the probability of getting two sets of 8-digit numbers with 5 digits being the same number and order, we need to break it down into steps.
Step 1: Determine the range of numbers for each digit.
In an 8-digit number, each digit can range from 0 to 9. However, since we have 5 fixed digits, we need to adjust the range for the remaining 3 digits. So, the range for the first 3 digits is also 0 to 9.
Step 2: Calculate the number of possibilities for the first set.
For the first set, we have 5 fixed digits (the same number and order) and 3 remaining digits. The fixed digits can only be chosen in one way, so we don't need to calculate the possibilities for them. However, the remaining 3 digits can be chosen from any of the 10 possible numbers (0 to 9). So, the number of possibilities for the first set is 10 * 10 * 10 = 1000.
Step 3: Calculate the number of possibilities for the second set.
For the second set, we have the same number and order for the first 5 digits as the first set. Additionally, the remaining 3 digits can also be chosen from any of the 10 possible numbers. So, the number of possibilities for the second set is also 10 * 10 * 10 = 1000.
Step 4: Calculate the total number of possible outcomes.
To find the total number of possible outcomes, we multiply the number of possibilities for the first set by the number of possibilities for the second set. So, the total number of possible outcomes is 1000 * 1000 = 1,000,000.
Step 5: Calculate the probability.
The probability is defined as the number of desired outcomes divided by the total number of possible outcomes. In this case, the desired outcome is 1 (getting two sets with 5 matching digits in the same order), and the total number of possible outcomes is 1,000,000.
Therefore, the probability of getting two sets of 8-digit numbers with 5 digits being the same number and order is 1/1,000,000 or 1 in 1,000,000.