If a+b+c=21, what is the total number of non-negative integral solutions?
Choose the correct answer:
A) 223
B) 233
C) 240
D) 243
E) 253

Rationale: think of it is a problem of diving 21 items to three people a , b & c which may or may not receive an item . so simply use combination here as ( n - r + 1 ) c ( r - 1 ) i . e . ( 21 + 3 - 1 ) c ( 3 - 1 ) = > 23 c 2 = = > 253 solutions . answer : e
Answer: E