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?

Consider ABCD ABCD

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

If ONE bag is selected 1000

If TWO bags are selected This is the same as 1000

1110 If THREE bags are selected 2100

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

If FIVE bags are selected

If SIX bags are selected This is the same as 1110

If SEVEN bags are selected 2221

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

Summing it up…… 1  1000= 4 2  = 6 3  = 12+ 4= 16 4  = = 13 5  = =16 6  = 6 7  2221= 4 8  2222= TOTAL 65

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?

If ONE bag is selected 1000

If TWO bags are selected This is the same as 1000

1110 If THREE bags are selected 2100

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

If FIVE bags are selected

If SIX bags are selected This is the same as 1110

If SEVEN bags are selected 2221

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

Summing it up…… 1  1000C(4, 1)= 4 2  1100C(4, 2)= 6 3  C(4, 2) C(2, 1) + C(4, 3) = 6 * 2+ 4= 16 4  C(4, 3) C(3, 1) + C(4, 4) = 4 * 3 + 1= 13 5  C(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  = TOTAL 65

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?

Consider ABCD ABCD ABCD

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

If ONE bag is selected 1000

If TWO bags are selected This is the same as 1000

2200 If FOUR bags are selected This is the same as

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

3200 If FIVE bags are selected

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

2221 If SEVEN bags are selected

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

If NINE bags are selected This is the same as 1110

If TEN bags are selected

If ELEVEN bags are selected 3332

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

Summing it up…… 1  1000= 4 2  1100= 6 3  = 16 4  = 25 5  =40 6  =34 7  = 40 8  =30 9  =16 10  =10 11  3332 = 4 12  = TOTAL 225

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?

10000 If ONE bag is selected

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

If THREE bags are selected

If FOUR bags are selected This is the same as 11000

If FIVE bags are selected 22100

If SIX bags are selected This is the same as 11100

If SEVEN bags are selected

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

22221 If NINE bags are selected

If TEN bags are selected This is the same as 11111

Summing it up…… 1  10000= 5 = 5 2  11000= 10 = 10 3  = = 30 4  = = 35 5  = =51 6  = =35 7  = = 30 8  22211= 10 =10 9  22221= 5 = 5 10  = TOTAL 211