Question

How many non- negative integral solution possible for equation below

x + y + z + w = 20

• A. ${}^{23}{C}_3$
• B. ${}^{22}{C}_2$
• C. ${}^{19}{C}_3$
• D. None of these

Answer 1

The correct option is A ${}^{23}{C}_3$

(x, y, z, w and integers can take value from 0 to 20). It is application of partion rule. 20 things to be distributed among x, y, z, w such that some values can be zero.
Hence total no. of non-negative integral solution.
${=}^{20+4-1}{C}_{4-1}{=}^{23}{C}_3$
Hence option (a)