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 Question from Greg, a parent: I need help with this question, and the explanations in books I have are confusing. Could someone help? I have six crayons: red, orange, yellow, green, blue, and purple. I need to know how many combinations of three crayons can I have. Thank you.

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

 R O Y G B P

Now select a second crayon. Whichever colour you chose first you have 5 choices for the second crayon. Hee are the possibilities.

 RO OR YR GR BR PR RY OY YO GO BO PO RG OG YG GY BY PY RB OB YB GB BG PG RP OP YP GP BP PB

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

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