POSSIBLE COMBINATIONS FOR 3 ITEMS

[brianaclark1967]

Hi Guys,

I have three items (3 types of doors), a single, a leaf & half and a Double

If I could sell a maximum of 10 double, 10 leaf & half and 20 single;

How many possible sales permutations could there be.

I've attached a sample sheet showing my query.

Many thanks

Brian

 

[NARAYANK991]

Hi Brian ,

Instead of using the designations , we can think of them as 3 categories :

Category 1 has 11 options from 0 through 10

Category 2 has 11 options from 0 through 10

Category 3 has 21 options from 0 through 20.

When you say permutations , I assume you actually mean combinations , since in permutations order matters ; thus , if you really mean permutations :

1 DD , 1 LH and 1 SD

would be different from

1 SD , 1 LH and 1 DD

If we go by combinations , then for every possibility in Category 1 , and for every possibility in Category 2 , we could have 21 possibilities of Category 3.

Thus , for the possibilities of 11 , 11 and 21 in the three categories , the number of combinations is 11 * 11 * 21 = 2541 - 1 = 2540 ; we exclude the combination of 0 , 0 , 0 since that is an irrelevant combination.

If you want to look at it another way , you can do it like this :

1. 20 combinations of SD
2. 10 combinations of LH
3. 10 combinations of DD

4. 20 * 10 = 200 combinations of SD and LH
5. 20 * 10 = 200 combinations of SD and DD
6. 10 * 10 = 100 combinations of LH and DD

7. 20 * 10 * 10 = 2000 combinations of SD , LH and DD

for a total of 2000 + 500 + 40 = 2540 combinations in all.

Narayan