The Rotokas of Papua New Guinea have twelve letters in their alphabet. The letters are: A, E, G, I, K, O, P, R, S, T, U, and V. Suppose license plates of five letters utilize only the letters in the Rotoka alphabet. How many license plates of five letters are possible that begin with either G or K, end with T, cannot contain S, and have no letters that repeat?
We have the avaiable letters
A E G I K O P R T U V
For the first letter, we can select either the G or K = 2 choices
For the next letter, we can pick one of 8 letters = 9 choices
For the next letter, can pick one of 7 letters = 8 choices
For the next letter, we can pick one of 6 letters = 7 choices
The last letter must be a "T"
So....2 * 9 * 8 * 7 = 1008 plates
EDIT to correct an errot