Convert Countif to array formula

Mmrtlm  ....  Your array-entered (?) COUNT formula is not the best way to do it, but it is a good first effort that can be made to work.

To understand why your does not, answer for yourself:  why does COUNT({1,0}) return 2?  Given that it does, what alternative function would return 1 instead?

PS....  You might use Formula Evaluation to see the operation of your COUNT formula.  Of course, try it with a much range of rows.

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For a better solution, explain for youself as if to someone else: what condition does COUNTIF($O$2:$O$9995,AA$11,$M$2:$M$9995,$Z$12,$X$2:$X$9995,$Z13) count as 1?

I would use nested IF expressions to make that happen in an array-entered formula.

But you seem to know how to use multiplication to effect an AND operation, since we cannot use AND itself in an array-entered formula and have it work as a row-by-row opertion.

Sorry, but since the assignment is to craft an array-entered formula, I cannot offer turnkey solutions or explanations.  After all, that is __your__ assignment to do.