permutations – Summation Translation – Mathematics Stack Exchange

I translated a sum of terms being multiplied into two summations being multiplied, but I’m not sure if the summation’s I’ve made matches the sum I originally had.

Original Equation: $frac{26!}{8!(26-8)!} + frac{26!}{7!(26-7)!}(frac{26!}{1!(26-1)!}) + frac{26!}{6!(26-6)!}(frac{26!}{2!(26-2)!}) + frac{26!}{5!(26-5)!}(frac{26!}{3!(26-3)!}) = 264,517,825$

My Summations: $sum_{n=8}^5 frac{26!}{n!(26-n)!} * sum_{i=0}^3 frac{26!}{i!(26-i)!}$

My calculator enters overflow mode when I try to check with that.