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 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.
To find the number of different ways Patrick can use his crayons to draw his picture, we need to consider that he can use a maximum of three colors from the given options.
Let's list out all the possible combinations:
1. Red, Blue
2. Red, Yellow
3. Red, Green
4. Red, Orange
5. Red, Purple
6. Blue, Yellow
7. Blue, Green
8. Blue, Orange
9. Blue, Purple
10. Yellow, Green
11. Yellow, Orange
12. Yellow, Purple
13. Green, Orange
14. Green, Purple
15. Orange, Purple
16. Red, Blue, Yellow
17. Red, Blue, Green
18. Red, Blue, Orange
19. Red, Blue, Purple
20. Red, Yellow, Green
21. Red, Yellow, Orange
22. Red, Yellow, Purple
23. Red, Green, Orange
24. Red, Green, Purple
25. Red, Orange, Purple
26. Blue, Yellow, Green
27. Blue, Yellow, Orange
28. Blue, Yellow, Purple
29. Blue, Green, Orange
30. Blue, Green, Purple
31. Blue, Orange, Purple
32. Yellow, Green, Orange
33. Yellow, Green, Purple
34. Yellow, Orange, Purple
35. Green, Orange, Purple
36. Red, Blue, Yellow, Green
37. Red, Blue, Yellow, Orange
38. Red, Blue, Yellow, Purple
39. Red, Blue, Green, Orange
40. Red, Blue, Green, Purple
41. Red, Blue, Orange, Purple
42. Red, Yellow, Green, Orange
43. Red, Yellow, Green, Purple
44. Red, Yellow, Orange, Purple
45. Red, Green, Orange, Purple
46. Blue, Yellow, Green, Orange
47. Blue, Yellow, Green, Purple
48. Blue, Yellow, Orange, Purple
49. Blue, Green, Orange, Purple
50. Yellow, Green, Orange, Purple
51. Red, Blue, Yellow, Green, Orange
52. Red, Blue, Yellow, Green, Purple
53. Red, Blue, Yellow, Orange, Purple
54. Red, Blue, Green, Orange, Purple
55. Red, Yellow, Green, Orange, Purple
56. Blue, Yellow, Green, Orange, Purple
57. Red, Blue, Yellow, Green, Orange, Purple
So, there are a total of 57 different ways Patrick can use his crayons to draw his picture.