I am trying to enter a formula to do the following:

I am trying to have one cell count the number of times a name appears in one
column while a value also appears in another alongside of it

Ex:

Column A Column B
Bill 1
Steve 1
Harry 0
Bill 1
Harry 1
Bill 0
Steve 1
........

I am looking for a formula that tells me how many times Bill appears in
column A and 1 appears in column B alongside it (has to be both Bill and 1)

The example above should give me a result of 2

Any suggestions?