COUNTIFS with OR condition

Hi

I have 3 columns. I want to count the number of 1s (could actually be 1-/1/1+) in column A and the number of 1s in EITHER columns B and C

so for e.g. if cell A1 contained 1 and celll B1 contained 2 and cell C1 contained 1 ... then the count would return 1

and if cell A1 contained 1 and cell B1 contained 1 and cell C1 contained 2 ... then the count would still return 1

I think I would need something like

=COUNTIFS($A$1:$A$40,"*1*",$B$1:$H$B40,"*1*",$C$1:$C$40,"*1*")

????? But would need an AND/OR condition for columns B and C.


Hope that makes sense and someone can help.

TIA