A toy company is making name plates for children. They will only use 6 spaces, and include only letters. How many combinations are possible?

1 Answer

#26xx26xx26xx26xx26xx26=26^6="308,915,776"# combinations.


I'll assume we're using the English alphabet, and so we have 26 letters to use. I'll also assume that we aren't going to exclude any words for any reason. Lastly, I'm going to assume we can repeat characters, and so AAAAAA, for example, is valid.

In each of the six spots, we can place any one of the 26 letters. This gives:

#26xx26xx26xx26xx26xx26=26^6="308,915,776"# combinations.