Combinatorics

Probability Level 3

How many distinct solutions are there for the equation x + y + z + w = 10 x+y+z+w=10 over non negative integers x , y , z , w x,y,z,w ?


The answer is 286.

Vilakshan Gupta by Vilakshan Gupta , 19, India

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1 solution

Md Zuhair
Aug 7, 2017

It is directly asked upon the topic Integer Equations .|

( 10 + 4 − 1 4 − 1 ) ⟹ ( 13 3 ) ⟹ 286 \dbinom{10+4-1}{4-1} \implies \dbinom{13}{3} \implies \boxed{286}

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