if a + b + c = 21 , what is the total number of non - negative integral solutions ?
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
divide(divide(factorial(add(21, const_2)), factorial(21)), const_2)