I'm having trouble finding the number of $6$ ordered letter sequences from a $4$-set (i.e. $\{a, b, c, d\}$), that contain at least one of each different letter.
Should it be $4\times 4\times 4!$ because there are $4\times 4$ ways to choose the first two letters, and then the next $4$ are the permutations of the set, or something else? I have a feeling I'm missing something...
Thanks!