How do you code the following situation:

countif(AND, logic1, logic2, logic3)

meaning I want it to count all of the occurances within three different
coloums of data.
Example: If Sally has a Doctors appointment in March, or If Mark has a
Tennis appointment in June, or if Bob has a dentist appointment in August. So
I want to be able to ask, how many doctors appointments does Sally have in
May? Or how many dentist appointments does Bob have in July.