Your password for a given website is made up of three letters followed by
four numbers. Find the number of possible passwords if there are no
restrictions on what three letters and what four numbers can be used.
Pls check if my answer is correct
26C3*10C4
=26!/(26-3)!3! . 10!/(10-4)!4!
= 26*25*24*23!/23!*6 . 10*9*8*7*6!/6!*4*3*2*1
=15600/6 * 5040/24
=2600*210
=546000
I didn't see that letters or numbers cant be used more than once.
26*26*26*26*10*10*10*10
As I read it AAAA0000 is allowed, your number didn't include those.
Thanks
To find the number of possible passwords, we need to determine the number of choices we have for each character in the password.
For the three letters, you can use any letter from the alphabet, which consists of 26 letters (assuming we are using only uppercase letters).
For the four numbers, we can use any digit from 0 to 9.
Now, let's calculate the number of possible passwords:
Number of choices for the first letter = 26
Number of choices for the second letter = 26
Number of choices for the third letter = 26
Number of choices for the first number = 10
Number of choices for the second number = 10
Number of choices for the third number = 10
Number of choices for the fourth number = 10
To find the total number of possible passwords, we multiply the number of choices for each character:
Total number of possible passwords = Number of choices for the first letter × Number of choices for the second letter × Number of choices for the third letter × Number of choices for the first number × Number of choices for the second number × Number of choices for the third number × Number of choices for the fourth number
Total number of possible passwords = 26 × 26 × 26 × 10 × 10 × 10 × 10
Calculating this expression gives us the final answer:
Total number of possible passwords = 26^3 × 10^4
Total number of possible passwords = 17,576,000
Therefore, there are 17,576,000 possible passwords without any restrictions on the three letters and four numbers.