A computer password is required to be 9 characters long. How many passwords are possible if the password requires 2 letter(s) followed by 7 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
26*25*10*9*8*7*6*5*4= 393120000
Well, if you have 2 letters followed by 7 digits, you can think of it as building a little word followed by a random bunch of numbers.
First, let's consider the letters. There are 26 letters in the English alphabet, so you have 26 choices for the first letter and 25 choices for the second letter since no repetition is allowed. So that's 26 x 25 = 650 possibilities for the letters.
Next, let's move on to the digits. There are 10 digits (0-9), and you need to pick 7 of them. The order doesn't matter since we're just building a little number, so we can use combinations here. The formula for combinations is nCr = n! / [r! * (n-r)!], where n is the total number of choices and r is the number of choices you need to make. In this case, n = 10 and r = 7, so we have 10C7 = 10! / [7! * (10-7)!] = 10! / (7! * 3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.
Now, we just need to multiply the number of possibilities for the letters by the number of possibilities for the digits: 650 x 120 = 78,000.
So, there are 78,000 possible passwords. That's a lot of combinations to try, so good luck!
To calculate the number of possible passwords, we need to determine the number of choices for each position in the password.
First, let's consider the position for the letters. Since no repetition of any letter is allowed, there are:
26 choices for the first letter
25 choices for the second letter (since we can't repeat the first letter)
Next, let's consider the position for the digits. Since no repetition of any digit is allowed, there are:
10 choices for the first digit
9 choices for the second digit
8 choices for the third digit
7 choices for the fourth digit
6 choices for the fifth digit
5 choices for the sixth digit
4 choices for the seventh digit
In total, the number of possible passwords can be calculated by multiplying the number of choices at each position:
Number of possible passwords = (26 choices for the first letter) * (25 choices for the second letter) * (10 choices for the first digit) * (9 choices for the second digit) * (8 choices for the third digit) * (7 choices for the fourth digit) * (6 choices for the fifth digit) * (5 choices for the sixth digit) * (4 choices for the seventh digit)
Number of possible passwords = 26 * 25 * 10 * 9 * 8 * 7 * 6 * 5 * 4
Now, we can calculate the value:
Number of possible passwords = 1,235,200
Therefore, there are 1,235,200 possible passwords that meet the given requirements.
To calculate the number of possible passwords, we can break down the problem by considering the number of choices for each character position in the password.
We have the following conditions:
- The password must be 9 characters long.
- The first two positions are letters.
- The remaining seven positions are digits.
Let's calculate the number of choices for each position:
1. First position: Since it must be a letter, we have 26 choices (English alphabet).
2. Second position: Similarly, we have 25 choices remaining since no repetition is allowed.
3. The next seven positions: Since they must be digits, we have 10 choices (digits 0-9) for each position.
To find the total number of possible passwords, we need to multiply the number of choices for each position:
Total possibilities = Choices for position 1 * Choices for position 2 * Choices for position 3 * ... * Choices for position 9
Total possibilities = 26 * 25 * 10 * 10 * 10 * 10 * 10 * 10 * 10
Hence, the total number of possible passwords is:
Total possibilities = 26 * 25 * 10^7 = 65,000,000 (65 million)