Find the number of non-negative integral solutions of equation `x+y+z+2w=20.`

Explanation

If w=0, equation reduces to x+y+z=20.
Number of non-negative inteegral solutions `= .^(20+3-1)C_(3-1) = .^(22)C_(2)`
If w=1, equation reduces to x+y+z=18.
Number of non-negative integral solutions `=(18+3-1)C_(3-1)= .^(20)C_(2)`
Similarly, we get number of non-negative integral solutions for w=2, 3, .., 10.
Hence, total number of solutions
`=(22)C_(2)+ .^(20)C_(2)+ .^(18)C_(2)+..+ .^(2)C_(2)`