Counting number of rows having a particular string in two different columns

Hello,

I have attached a sample of the data I'm working with. Basically, I would like to count the number of rows in my table that:

1) Contain the string "sprit" in column B,

AND

2) Do not hav "no-DNA profile" on column A.

I've been using the following formula to count the number of rows having "no-DNA profile" on column A:

=COUNTIF(A1:A1183,"no DNA-profile")

And when substracting that and the total number of empty cells to the total number of cells in the table, I've been able to count the number of rows responding to criteria 2). However, I'm unsure about how to add a second level of complexity to my formula by counting the number of rows also fulfilling criteria 1).

If somebody could at least set me on the right track, that would be truly appreciated!