(i) ( \dfrac{10!}{0!,8!} )

[ \dfrac{10!}{0!,8!} = \dfrac{10\times 9\times 8!}{1\cdot 8!} = 90. ]

Answer: ( 90 )

(ii) ( \dfrac{12!}{3!(12-3)!} )

[ \dfrac{12!}{3!,9!} = \dfrac{12\times 11\times 10\times 9!}{6\times 9!} = \dfrac{12\times 11\times 10}{6} = 220. ]

Answer: ( 220 )

(iii) ( \dfrac{1440}{3!,4!} + \dfrac{2400}{5!,2!} )

[ 3! = 6,\ 4! = 24,\ 5! = 120,\ 2! = 2. ] [ \dfrac{1440}{6\times 24} + \dfrac{2400}{120\times 2} = \dfrac{1440}{144} + \dfrac{2400}{240} = 10 + 10 = 20. ]

Answer: ( 20 )

(iv) ( \dfrac{(n+2)!}{(n+1)!} )

[ \dfrac{(n+2)!}{(n+1)!} = n+2. ]

Answer: ( n+2 )