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.

Answer 1

Make a list of all the three-color 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.