Find the number of ways to distribute 20 identical aam s among 4 aam lovers such that each aam lover receives atleast one aam.

The word 'aam' comes from the Hindi language meaning a mango.

The answer is 969.

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With $a_{n}$ representing the number of aams the $n$ th aam lover receives, we must find the number of positive integer solutions to the equation

$a_{1} + a_{2} + a_{3} + a_{4} = 20.$

This is a stars and bars calculation, which according to Theorem one in the link has solution

$\dbinom{20 - 1}{4 - 1} = \dbinom{19}{3} = \boxed{969}.$