Jose is choosing a 3-letter password from the letters a, b,c, d. the password cannot have the same letter repeated in it. how many passwords are possible

Alright, so we are dealing with permutations. Permutations are the number of combinations in a specific order possible for the set. 

There's 4 letters, each one can be paired with 3 other letters, but those letters could be in different orders. To figure out how many variations of each combination there are (aka the number of permutations) use this formula:



number of elements in the subset

number of elements in the set

permutations of the set

There are only 3 elements in the subset because there is 1 that will not be repeated in each set, and there are 4 elements in the set.

Here's the math:











There are 24 permutations. I can prove this by showing you the model:

ABCD, ABDC, ACBD, ACDB, ADBC, ADCB are the 6 arrangements possible of the set starting with the letter A. Because there are 4 letters, the total amount of permutations without repeated letters is 4 (letters) times 6 (possible arrangements), which equals 24.

Hope this helps!

24 passwords are possible