COUNTIFS(...)
How to countif between a date range
Used Functions
Category: Statistical
Counts the number of cells within a range that meet multiple criteria
Syntax
COUNTIFS(criteria_range1, criteria1, [criteria_range2, criteria2]…)
Practice COUNTIFS Formula at Sheetzoom
COUNTIFS formula at Microsoft help
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Here COUNTIFS take two arguments as criteria, one as a lower bound ensuring that no date is selected lower to it, and the upper bound as second criteria to make sure every thing is less then it. There are two lookup ranges respectively to get the count.