teresa has to create a password that contains 1 digit and 2 letters. find the number of possible passwords?
how do you do this?
i did 26 *26*9 because there are 26 letters in an alphabet, and just 1 letter can go into 26 (counting its self) and 9 because it has to be 1 number.
so 26*26*9=6084
I will assume that zero can be used as a digit, and that letters can repeat.
There are 3 ways for the digit and letters to show up
DLL
LDL
LLD
let's find the number of ways DLL can be done
= 10x26x26
the same with the other two, so the number of ways is
3(10)(26)(26) = 20280
To find the number of possible passwords, we need to consider the number of choices for each component of the password.
Step 1: Select the digit:
Since Teresa is required to have 1 digit in her password, she has 10 options (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
Step 2: Select the first letter:
Teresa needs to choose 1 letter for the first position in her password. There are 26 options (A, B, C, ..., Z) for the first letter.
Step 3: Select the second letter:
Similarly, Teresa needs to choose 1 letter for the second position in her password. There are 26 options for the second letter as well.
Now, to find the total number of possible passwords, we multiply the number of choices for each step:
Number of possible passwords = Number of choices for the digit * Number of choices for the first letter * Number of choices for the second letter
Number of possible passwords = 10 * 26 * 26
Calculating this value:
Number of possible passwords = 6,760
Therefore, Teresa has 6,760 possible passwords to choose from.