Counting non-zero cells across multiple columns with changing criteria

Hi,

Struggling to get my head around a COUNTIF >0 when spread across multiple columns and the columns to count can change from a drop down menu, whilst ensuring that I don't double count rows where they have data within multiple columns.

Hopefully this makes sense in the example below:

Column
A B C
0 1 0
1 0 1
0 0 2
0 0 0

Cell A1 is a drop down list: A, B, C, AB, AC, BC

In cell B1 I am looking for a formula that will tell me, based on cell A1, how many of the rows are not zero.

For example if A1 = BC
Then the result in B1 would be = 3 (3 of the rows have a number that is not zero in columns B or C.

If A1 = B then B1 = 1 because only one row has a number that is not zero in column B

If A1 = AC the B1 = 2 because only two rows have a number that is not zero in columns A or C. Note that row 2 is only counted once despite having a number in columns A AND C.

I am prepared that I may need some helper cells to make this possible.

Thanks for helping me with this brain teaser!!!

Thanks so much. No way I could have discovered that solution without your help. I went with the array formula that works a treat.