We have two responses for you

Greg,

You have 6 different choices, but only 3 choices to make.
__ __ __
How many options do you have on your first choice?
6_ __ __
Now, how many options do you have for your second choice? (remember you already chose once)
6_ 5_ __
Now how many options does that leave you for your third choice?
6 5_ _?_
Now multiply your three choices together
6 * 5 * ? =
This is the number of combinations you can make of 3 when you have 6 choices.

Good Luck
Melanie

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,
Penny