Aam lelo aam

Probability Level 3

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.

Rohit Ner by Rohit Ner , 22, India

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1 solution

With a n a_{n} representing the number of aams the n 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. 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

( 20 − 1 4 − 1 ) = ( 19 3 ) = 969 . \dbinom{20 - 1}{4 - 1} = \dbinom{19}{3} = \boxed{969}.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

The stars and bars is a cool method! Thank you for posting! :)

Rohit Ner - 6 years ago

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You're welcome. :) Yes, stars and bars is an indispensable method.

Brian Charlesworth - 6 years ago

Done the same

Ravi Dwivedi - 5 years, 11 months ago

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