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?

Logic  Oct 18, 2018

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



cool cool cool

CPhill  Oct 18, 2018
edited by CPhill  Oct 18, 2018

CPhill, didn't you forget about the V?

KnockOut  Oct 18, 2018

Thanks, Knockout...I have made the correction !!!


cool cool cool

CPhill  Oct 18, 2018

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