Excel Array Formula multiple criterias for sum

Customer    Amount    Date
1             10         10/02/2019
2             20         10/02/2019
3             30         11/04/2019
4             40         11/04/2019
1             50         10/02/2019
2             60         10/10/2019
2             70         11/04/2019
2             80         11/04/2019

I wanted to write an excel array formula that is basically sumifs. The reason I cant use the sumifs formula is because I would like to use the Mouth() formula on the date but it doesn't seem to work.

I tried writing this array formula but I come up with the answer of 0. The correct result should be 80

{=SUM(IF(AND(MONTH($C$1:$C$8)=10,$A$1:$A$8=2),$B$1:$B$8,0))}

I know I could probably use a helper column to turn the date to the month and sumif based on that, but I wanted to keep my report neat and to learn arrays in general.

Thank you!