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Default Formula to count TWO conditions are met

I am relatively new to formulas with Excel. I have used 'COUNTIF' to count
how often a coloumn contains a certain line of text. However I want a formula
which will do the following (with a made up example);
Coloumn A is a pick-list of names - e.g. A Nother, J Bloggs etc
Coloumn B is a pick-list of queries - e.g. Late for Work, Sickness Day etc
I need to create a formula that would count how often the combination of 'A
Nother' & 'Sickness Day' was used, and another for how often the combination
of 'Joe Bloggs' and 'Late for work' was also used. This is for use in a table
& chart.

Many thanks.
 
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