Question

Find the number of solutions of x + y+ z = 17, where x, y, z are non negative integers such that x ϵ [2,5], y ϵ [3,6], z ϵ [4,7].
Mathdude answer please​

Answer 1

Let us take an example; x + y = 10 and we have to find out a number of  whole number solutions of it,

we can approach in this way, we have and

Therefore, number of arrangements = 11!/(10!) =11

hence, the number of whole number solutions= 11 which there are 11 ways in which we can assign a value to x and y so that sum will be equal to 10.

Similarly, we can break this question too;

x + y + z !)= 171

Hence there are 171 ways in which we can assign a value of x,y and z so that sum will be equal to 17

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Answer 2

Step-by-step explanation:

x+y+z=10

x,y,z⟶ positive

Number of Non negative for

x,y,z⟶ positive

⇒x

x+y+z=10⟶for

⇒a=x−1

⇒b=y−1

⇒c=z−1

a,b,c⟶non negative integer

⇒a+b+c=7

⇒n=7

⇒r=3

Therefore number of possible solutions are

⇒

7+3−1

it's Isha