Counting non-Negative Integer Solutions to x + y + z = 21 with Constraints

Anybody who knows how to count numbers of possible distributions of IDENTICAL objects (such as candies or apples) between DISTINCT recipients (such as people or numbered boxes) also knows how to count the number of non-negative integer solutions to equations such as x + y + z = 21, even though they may not realise it.

After watching this video, answering the two types of questions will hopefully be equally simple, which is good news because these types of questions are a mainstay of Maths Olympiads and College Entrance Exams.

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