Question

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?

Answer 1

12 letters in all but less "S" which is not allowed. That leave 11 usable letters, of which 5 distinct letters are used for each plate.

begins with G or K (2 choices). That leaves 10 letters.

Ends with T (1 choice). That least 9 for the middle letters.

Second letter (9 choices)

Third letter (8 choices)

Fourth letter (7 choices)

Total number of licence plates

=product of choices of letters for each position

= 2*9*8*7*1

=1008