Question

тема факториал
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Answer 1

 

$1) frac{h(h-1)(h-2)(h-3)(h-4)}{(h-3)!} = frac{h(h-1)(h-2)(h-3)(h-4)}{1*2*...*(h-4)*(h-3)} =\ frac{h(h-1)(h-2)}{1*2*...*(h-5)} = frac{h!}{(h-5)!(h-3)!}$

 

 

$2) frac{10! - 8!}{89} = frac{8!(9*10 -1)}{89} = 8! = 40320\\ 3) frac{5! + 6!}{4!} = frac{4!(5 +5*6)}{4!} = 35\\ 4) A^{m-5}_{m-1} = frac{(m-1)!}{(m-1-m+5)!} = frac{(m-1)!}{4!} = frac{(m-1)!}{24}$