how many natural solutions exist to x+y+z=11, x,y,z∈N


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Question Number 46760 by arcana last updated on 31/Oct/18

$h o w m a n y n a t u r a l s o l u t i o n s e x i s t$ $t o$ $x + y + z = 11, x, y, z \in N$
Commented by MrW3 last updated on 31/Oct/18

$n o . o f w a y s t o p u t 11 o b j e c t s i n t o 3 c o n t a i n e r s :$ $C_{2}^{10} = 45$
	Answered by Kunal12588 last updated on 31/Oct/18

	$l e t s t r y$ $1 + 1 + 9 (1)$ $1 + 2 + 8 (2)$ $1 + 3 + 7 (3)$ $1 + 4 + 6 (4)$ $1 + 5 + 5 (5)$ $2 + 2 + 7 (6)$ $2 + 3 + 6 (7)$ $2 + 4 + 5 (8)$ $3 + 3 + 5 (9)$ $3 + 4 + 4 (10)$ $4 + 5 + 2 = 2 + 4 + 5 c o u n t e d b e f o r e$ $t o t a l = 10$
	Commented by arcana last updated on 31/Oct/18

	$can you proof it ?$
	Commented by arcana last updated on 31/Oct/18

	$x, y, z \neq 0 sorry$
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