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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?

 Oct 18, 2018
 #1
avatar+98091 
+1

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

 Oct 18, 2018
edited by CPhill  Oct 18, 2018
 #2
avatar+624 
+10

CPhill, didn't you forget about the V?

KnockOut  Oct 18, 2018
 #3
avatar+98091 
0

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

 

cool cool cool

CPhill  Oct 18, 2018

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