15.) Consider the regular hexagon shown. (a) In how many ways can the vertices be labelled with a distinct letter of the alphabet? P( 26,6 ) = 26! 201 = 165765 600 (b) How many different triangles can be formed inside the hexagon by connecting 3 of the vertices? 6 ! ( (6. 3 ) = 3 ! 3 ! = 20 (c) (optional extra credit) In how many ways can the vertices be labelled with a distinct letter of the alphabet if the top right vertex must be labelled P or Q, and three of the other letters must be A,B,C