How many strings of length 5 can be written using the letters {a,b,c,d,e,f} if no two consecutive letters can be the same? For example, we'd count adede but not acdde.

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.