



 
We have two responses for you Greg,
Greg, I am going to represent the colours by R, O, Y, G, B and P. Think about actually doing this with crayons. First you select a first crayon. Here are the possibilities
Now select a second crayon. Whichever colour you chose first you have 5 choices for the second crayon. Hee are the possibilities.
Thus each of the 6 possibilities for a 1 crayon combination expands into 5 possibilities for a 2 crayon combination. Hence there are 6 × 5 = 30 possible 2 crayon combinations. Finally the third crayon. Regardless of which of the 30 combinations above constitutes the first 2 crayons, there are 4 choices left for the third crayon. Thus if you are listing all the possibilities then each of the 30 above expands into 4 possibilities for a 3 crayon combination. Hence there are 30 × 4 = 6 × 5 × 4 = 120 possible 3 crayon combinations. I hope this helps,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 