Question

No. of solutions to the following inequality 12 <= w + x + y + z <= 14 where w,x,y,z>=0

Comments

The Idea I have is to solve this is:

(no. of solution for w + x + y + z = 12) + (no. of solution for w + x + y + z = 13) + (no. of solution for w + x + y + z = 14)

= 15C3 + 16C3 + 17C3

= 1695

is it correct?

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@Deepak Poonia sir please look into this

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That’s correct @khushitshah .

Answer 1

One of the method is have cases

Case 1: w+x+y+z = 12

Case 2: w+x+y+z = 13

Case 3: w+x+y+z = 14.

Upon applying IODB – star bar template
no of solutions = = 15C3 + 16C3 + 17C3