The number of non-negative integral solutions of `x+y+z<=n,` where `n in N` is

Options

A. `""^(n+3)C_(3)`
B. `""^(n+4)C_(4)`
C. `""^(n+5)C_(5)`
D. none of these

Explanation

Let u be a variable such that x+y+z+u=n. Then,
`x+y+zlenimpliesugt0`.
The number of non-negative integral solutions of the given inequations is same as the number of non-negative intergral solutions of x+y+z+u=n. Hence,
The required number of solutions `=""^(n+4-1)C_(4-1)=""^(n+3)C_(3)`.