Number of Non-Negative Integer solutions of the equation x + y + z = 10 | General Case Explained

In this video, we count how many non-negative integer solutions are there for the equation x+y+z=10. In general, if x+y+z=n, how many such solutions will be there? That also explained. Also explained in general, the number of non negative integer solutions of the equation x_1 + x_2 +... + x_r = n.
A generalized idea of how to attack this problem is mentioned.
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[@Rtistanand]

very helpful sir

[@taraa282]

Wonderful explanation 🔥🔥👌🏻👌🏻👌🏻👌🏻

[@user-rm9oi2jd8r]

ty dude v good explanation

[@daksheshdoshi7007]

Thanks

[@thePRECIOUS_1]

A gem of explanation.

[@learnwithsreyas1777]

Thank you!

[@tapeface2863]

well explained

[@unnumemisto05]

10/10 very helpful 😅

[@L.animas]

Very well explained!👏👏👏

[@learnwithsreyas1777]

Thank you!

[@btbbbiologythebrainbuffer6012]

🎉🎉🎉 clear

[@peramvenkatasivapavani3990]

1. Three variables x,y,z have sum of 30.
All three of them are non- negative
integers. If any two variables don't have
same value and exactly one variable has
a value less than or equal to three, then
find the number of possible solution for
variables.

[@peramvenkatasivapavani3990]

May I know the answer for this

[@learnwithsreyas1777]

@@peramvenkatasivapavani3990 how much did you get?

[@peramvenkatasivapavani3990]

@@learnwithsreyas1777 according to your process I got 496 and I don't the correct answer

[@learnwithsreyas1777]

@@peramvenkatasivapavani3990 496 is the general solution when the only restriction is that x,y and z are non negative integers.

[@learnwithsreyas1777]

@@peramvenkatasivapavani3990 since you also have other restrictions like exactly one variable less than or equal to 3, and other two variables having not the same value, answer will change, have to consider these restrictions. I have done it, and got 252 as the answer.

[@pavanfernandes9329]

The marker sound making uncomfortable, I hope some might have the same problem. May be Change marker or board would be nicer.

[@learnwithsreyas1777]

Okay. Sure.