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?

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