@tanveer-malhotra As a+b+c+d+e+f < = 17, implies it can vary from (6,16)

To solve the inequality and make it into an equation, he considered a dummy variable g such that

a+b+c+d+e+f+g = 17. g can vary from 0 to 11.

In the above equation, a,b,c,d,e,f vary from 1 to 6 while g varies form 0 to 11.

To bring them on a common platform, we assume a,b,c,d,e,f having an initial value of 1, which makes the equation a+b+c+d+e+f+g = 11 where all start at 0.

total solutions for this is 11+7-1 C 7-1 which 17 C 6.

However, we have to subtract cases of a,b,c,d,e,f exceeding 6.

For that , take a has taken a value of 6,

so a+b+c+d+e+f+g = 11-6 = 5.

Invalid cases for a is 5+7-1 C 7-1 which is 11C6.

consider the invalid cases for all variables which is 11C6 * 6.

and now subtract it from the actual cases.