Carmen is choosing a
3
-letter password from the letters A, B, C, and D. The password cannot have the same letter repeated in it. How many such passwords are possible?
there are 4 choices for the 1st letter
since that letter is used, there are only 3 choices for the 2nd letter.
So, extending that logic, the number of possible passwords is 4*3*2 = 24
Ah, password problems! They can be quite puzzling, can't they?
Let's try to figure this out. So, Carmen wants a 3-letter password without any repeated letters, using the letters A, B, C, and D.
For the first letter, she can choose from any of the 4 letters. After she picks her first letter, she has 3 remaining letters to choose from for the second letter. Finally, for the third letter, she has 2 remaining letters to choose from.
Using the fundamental principle of counting, we can multiply these choices together:
4 choices for the first letter * 3 choices for the second letter * 2 choices for the third letter = 24 possible passwords.
So, Carmen has 24 possible passwords to choose from. Happy password picking!
To find the number of possible passwords, we can use the concept of permutation.
Step 1: Determine the total number of available letters.
In this case, Carmen has 4 letters to choose from: A, B, C, and D.
Step 2: Determine the number of possible passwords.
Since Carmen is choosing a 3-letter password without repetition, we need to calculate the permutation of 4 letters taken 3 at a time.
The formula for permutation is:
P(n, r) = n! / (n - r)!
Here, n is the total number of available letters (4) and r is the number of letters chosen for the password (3).
Using the formula, we can calculate the permutation as follows:
P(4, 3) = 4! / (4 - 3)!
P(4, 3) = 4! / 1!
P(4, 3) = (4 × 3 × 2 × 1) / (1)
P(4, 3) = 24 / 1
P(4, 3) = 24
So, there are 24 possible passwords Carmen can choose from.
To find out the number of possible passwords, we can break down the problem into three steps:
Step 1: Choose the first letter of the password
Since Carmen cannot repeat any letters, she has four options for the first letter: A, B, C, or D.
Step 2: Choose the second letter of the password
Once Carmen has chosen the first letter, she has three options left for the second letter. She cannot choose the same letter that she chose for the first letter. Therefore, for each choice of the first letter, she has three options for the second letter.
Step 3: Choose the third letter of the password
Similar to the second step, Carmen has two options left for the third letter, as she cannot choose the same letter again.
To find the total number of passwords, we multiply the number of options for each step:
4 options for the first letter x 3 options for the second letter x 2 options for the third letter = 4 x 3 x 2 = 24
Therefore, there are 24 possible passwords that Carmen can choose.