The number of ways of getting a sum 16 on throwing a dice four times is______

Step-by-step solution

aligned & (x^1+x^2 +x^6 )^4 & x^4 ( 1-x^6 1-x )^4 & x^4 (1-x^6 )^4 (1-x)⁻⁴ & x^4 [1-4 x^6+6 x¹² . ] [(1-x)⁻⁴ ] & (x^4-4 x¹⁰+6 x¹⁶ )(1-x)⁻⁴ & (x^4-4 x¹⁰+6 x¹⁶ ) (1+ 15 12 x¹²+ ^9 C₆ x^6 . ) & ( 15 12 -4 ^9 C₆+6 ) x¹⁶ & ( ¹⁵ C₃-4 ^9 C₆+6 ) & =35 13-6 8 7+6 & =455-336+6 & =125 aligned