What is the total number of possible unique blends given:
1. 148 different teas that can be used in your blend
2. Blends can consist of either 2 or 3 different teas
3. Each tea in your blend can come in 10, 20, 30, 40, 50, 60, 70, 80, or 90% increments
4. There are 13 different accents (inclusions) that you may choose from
5. allowed up to 3 different accents to be added to each blend

Question

What is the total number of possible unique blends given:
1. 148 different teas that can be used in your blend
2. Blends can consist of either 2 or 3 different teas
3. Each tea in your blend can come in 10, 20, 30, 40, 50, 60, 70, 80, or 90% increments
4. There are 13 different accents (inclusions) that you may choose from
5. allowed up to 3 different accents to be added to each blend

kropot72 · Answer

The number of combinations of blends is 148C2 + 148C3
There are 9 increments in each tea. In the blend of two different teas the number of combinations of increments is 9 * 9. In the blend of three different teas the number of combinations of increments is 9 * 9 * 9.
The number of combinations of accents for each blend is 13C3.
The total number of unique blends is:
(148C2 * 81 * 13C3) + (148C3 * 729 * 13C3)