1. Grass Seed Problem A landscaper wanted to sow a blend of grass seed on a homeowner’s lawn. The landscaper had available two boxes each of 4 different types of grass seed. If the landscaper could only mix full boxes of the grass seeds in the blend, how many different blends of grass seed could the landscaper use?

2. Consider ABCD ABCD

3. AA =A AABB =ABAB AABBCCDD =ABCDABCD Some note: AABBCC =ABCABC

4. If ONE bag is selected 1000

5. If TWO bags are selected 11002000 This is the same as 1000

6. 1110 If THREE bags are selected 2100

7. 2200 If FOUR bags are selected 11112110 This is the same as 1100

8. If FIVE bags are selected 21112210

9. If SIX bags are selected 22112220 This is the same as 1110

10. If SEVEN bags are selected 2221

11. If EIGHT bags are selected 2222 This is the same as 1111

12. Summing it up…… 1  1000= 4 2  1100 2000= 6 3  2100 1110 = 12+ 4= 16 4  2111 1111 2200= 12 + 1= 13 5  2210 2111= 12 + 4 =16 6  2211 2220= 6 7  2221= 4 8  2222= 0 -------- TOTAL 65

13. Grass Seed Problem A landscaper wanted to sow a blend of grass seed on a homeowner’s lawn. The landscaper had available two boxes each of 4 different types of grass seed. If the landscaper could only mix full boxes of the grass seeds in the blend, how many different blends of grass seed could the landscaper use?

14. If ONE bag is selected 1000

15. If TWO bags are selected 11002000 This is the same as 1000

16. 1110 If THREE bags are selected 2100

17. 2200 If FOUR bags are selected 11112110 This is the same as 1100

18. If FIVE bags are selected 21112210

19. If SIX bags are selected 22112220 This is the same as 1110

20. If SEVEN bags are selected 2221

21. If EIGHT bags are selected 2222 This is the same as 1111

22. Summing it up…… 1  1000C(4, 1)= 4 2  1100C(4, 2)= 6 3  2100 1110 C(4, 2) C(2, 1) + C(4, 3) = 6 * 2+ 4= 16 4  2111 1111 C(4, 3) C(3, 1) + C(4, 4) = 4 * 3 + 1= 13 5  2210 2111C(4, 3) C(3, 2) + C(4, 4) C(4, 1) = 4 * 3 + 1* 4 =16 6  2211C(4, 4) C(4, 2) = 1 * 6= 6 7  2221C(4,4) C(4,3) = 1 * 4= 4 8  = 0 -------- TOTAL 65

24. Grass Seed Problem A landscaper wanted to sow a blend of grass seed on a homeowner’s lawn. The landscaper had available three boxes each of 4 different types of grass seed. If the landscaper could only mix full boxes of the grass seeds in the blend, how many different blends of grass seed could the landscaper use?

25. Consider ABCD ABCD ABCD

26. AA =A AAABBB =ABAB AAABBBCCCDDD =ABCDABCD Some note:

27. If ONE bag is selected 1000

28. If TWO bags are selected 11002000 This is the same as 1000

29. 2200 If FOUR bags are selected 11112110 This is the same as 1100 3100

30. 1110 If THREE bags are selected 21003000 This is the same as 1000

31. 3200 If FIVE bags are selected 211122103110

32. 3300 If SIX bags are selected 311122113210 This is the same as 1100

33. 2221 If SEVEN bags are selected 331032203211

34. 2222 If EIGHT bags are selected 332033113221 This is the same as 1111

35. If NINE bags are selected 333033213222 This is the same as 1110

36. If TEN bags are selected 33313322

37. If ELEVEN bags are selected 3332

38. If TWELVE bags are selected 3333 This is the same as 1111

39. Summing it up…… 1  1000= 4 2  1100= 6 3  2100 1110 = 16 4  3100 2110 1111 = 25 5  3200 3110 2210 2111 =40 6  3210 3111 2211 =34 7  3310322032112221= 40 8  332033113221=30 9  33213222=16 10  33313322 =10 11  3332 = 4 12  = 0 -------- TOTAL 225

41. Grass Seed Problem A landscaper wanted to sow a blend of grass seed on a homeowner’s lawn. The landscaper had available two boxes each of 5 different types of grass seed. If the landscaper could only mix full boxes of the grass seeds in the blend, how many different blends of grass seed could the landscaper use?

42. 10000 If ONE bag is selected

43. 11000 If TWO bags are selected 20000 This is the same as 10000

44. 2100011100 If THREE bags are selected

45. 211001111022000 If FOUR bags are selected This is the same as 11000

46. 2111011111 If FIVE bags are selected 22100

47. 221102111122200 If SIX bags are selected This is the same as 11100

48. 2221022111 If SEVEN bags are selected

49. 22211 If Eight bags are selected 22220 This is the same as 11110

50. 22221 If NINE bags are selected

51. If TEN bags are selected 22222 This is the same as 11111

52. Summing it up…… 1  10000= 5 = 5 2  11000= 10 = 10 3  11100 21000 = 10 + 20 = 30 4  11110 21100 = 5 + 30 = 35 5  11111 21110 22100= 1 + 20 + 30 =51 6  21111 22110= 5 + 30 =35 7  22111 22210= 10 + 20 = 30 8  22211= 10 =10 9  22221= 5 = 5 10  = 0 -------- TOTAL 211