Answer:
3750 strings.
Step-by-step explanation:
First we have 6 different letters to choose from (a, b, c, d, e, f) and we will make a string of length 5.
First, we would have to choose one of the letters, to do this we would have 6 choices.
For our second choice, we can only choose from 5 letters since we cannot choose the one that we already chose (no two consecutive letters can be the same).
Then, for our third choice, we would have to choose from 5 different letters (any letter but the one before).
Similarly for our fourth and fifth choice, we can choose 5 different letters.
Then, the total amount of strings would be:
6 x 5 x 5 x 5 x 5 = 6 x 5⁴ = 3750 strings.
