Question
The number of non negative integral solutions of equation 3x + y + z = 24
- 117
- 107
- 97
- None of these
The correct answer is: 117
3x + y + z = 24, x 
0, y 0, z 0
Let x = k 
y + z = 24 – 3k …(1)
24 – 3k 0 k 
8
0 k 8
For fixed value of k the number of solutions of (1) is
24–3k+2–1C2–1
= 25–3kC1
= 25 – 3k
Hence number of solutions
= 25 × 9 – 
= 225 – 108 = 117.
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