Question

1) 6!*14!/8!
2)12!+12-12!/13!
3)$C ^{98} _{100}$

Answer 1

$\frac{6!\cdot 14!}{8!}=\frac{6!\cdot14!}{6!\cdot 7\cdot 8}=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 9\cdot 10\cdot 11\cdot 12\cdot 13\cdot 14=\\\\=1556755200\\\\12!+12-\frac{12!}{13!}=12(11!+1)-\frac{1}{13}=\frac{156(11!+1)-1}{13}\\\\\\c_{100}^{98}=C_{100}^{100-98}=C_{100}^2=\frac{100\cdot 99}{2!}=4950$