ExcelBanter - Permutations with conflicting groups

Hi,
I wish to find only the number of permutations of the following example. There are 4 employees who are able to perform different tasks. If they are working one task, they cannot work on another.

Task#1 Task#2 Task#3
****** Alice Alice
Betty Betty Betty
Carol Carol ******
Denise ****** ******

Eg: Alice can only perform Task#2 or Task#3
Eg; Betty can perform either Task#1 or Task#2 or Task#3
Eg: Carol can perform Task#1 or Task#2
Eg: Denise can only perform Task#1

There are 7 combinations of tasks that can be achieved.

Betty Carol Alice
Carol Alice Betty
Carol Betty Alice
Denise Alice Betty
Denise Betty Alice
Denise Carol Alice
Denise Carol Betty

All I need to know is the solution "7". I do not need to know the different combinations. I wish to perform this calculation on an EXCEL spreadsheet without using macros and VBA.

On another board, I was kindly given the formula
(B+C+D)*(A+B+C)*(A+B)
This gives me a solution of sorts but I cannot seem to sort the wheat from the charf.

Once I can find a solution, I wish to expand it to a larger set of tasks and people.

I have spent ages on this and are really looking for help.
Regards

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