math
posted by chase .
Ms. Davis asked her students to draw a picture describing their hobby, She asked them to use only 3 colors. Patrick has a box of crayons containing the colors red, blue, yellow, green, orange and purple. How many different ways can Patrick use his crayons to draw his picture? Make an organixed list.

Make a list of all the threecolor combinations you can think of. There should be 6!/3! = 72/6 = 16.
First list the combinations with red
RBY
RBG
RBO
RBP
RYG
RYO
RYP
RGO
RGP
ROP
Now list the combinations with no red.
BYG
BYO
BYP
BGO
BGP
BOP
Can you think of any others? Rearrangements of the same three colors do not count.