Distributing IDENTICAL Objects between DISTINCT Recipients with Upper and Lower Limit Constraints

Maths Olympiads, College Entrance Exams and High School exams are replete with questions on distributing Identical/Distinct objects (such as candies, tasks etc) between Distinct/Identical recipients (such as people, bins, boxes etc).

One of the most difficult parts of answering these types of questions is knowing which mathematical formula to use and this depends principally on whether the objects and recipients are identical or distinct, because they lead to completely different methods and answers.

In this video we explain how to deal with IDENTICAL candies distributed between DISTINCT children C1, C2, C3 and C4 where there are both lower and upper constraints on how many candies two of the children are allowed.

As we show in the video, we can deal with both the upper and lower constraints by a slight tweaking of the basic 'stars and bars' method for counting identical objects between distinct recipients. Be careful of the possible double counting which we explain at 3:20.

which is a slightly easier version of the same question without the upper constraint.

For more videos on identical/distinct counting see our playlist 'Counting Identical/Distinct Distributions'

For more videos on counting see our playlist 'Counting'

For more videos on permutations and combinations, see our playlist 'Perms and Combs'

For more videos on Maths Olympiads see our playlist 'Maths Olympiads'

For more JEE Aspirant videos see our playlist 'JEE Aspirants'

For more videos on College Entrance Exams, see our playlist 'UPCAT and other CETS'

[karan]

The clarity you've given me today
you sir 've got my respect