Using Binomial theorem , our formula will be
{Σ (k = 0 to 6) 6!/[(6-k)! k!] } + {Σ (k=0 to 7) 7!/[(7-k)! k!] } + {Σ (k=0 to 8) 8!/[(8 - k)! k!]}
Next is simplify them
2 [6!/(6! 0!) + 6!/(5! 1!) + 6!/(4! 2!) + 7!/(7! 0!)+ 7!/(6! 1!)+ 7!/(5! 2!)+ 7!/(4! 3!) + 8!/(8! 0!) + 8!/(7! 1!) + 8!/(6! 2!) + 8!/(5! 3!)] + 6! /(3! 3!) + 8!/(4! 4!)
2 ( 1 + 6 +15 + 1 + 7 + 21 + 35 + 1 + 8 + 28 + 56) + 20 + 70
=448
