Question

calcule 7! sobre 3!
10! sobe 3! 7!
12! 3! sobe 15!

Answer 1

$n!=n\cdot(n-1)\cdot(n-2)\cdot(n-3)\cdot...\cdot3\cdot2\cdot1\\n!=n\cdot(n-1)!=n\cdot(n-1)\cdot(n-2)!=...$
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$\dfrac{7!}{3!}=\dfrac{7\cdot6\cdot5\cdot4\cdot3!}{3!}\\\\\\\dfrac{7!}{3!}=7\cdot6\cdot5\cdot4\\\\\\\boxed{\boxed{\dfrac{7!}{3!}=840}}$
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$\dfrac{10!}{3!7!}=\dfrac{10\cdot9\cdot8\cdot7!}{3!7!}\\\\\\\dfrac{10!}{3!7!}=\dfrac{10\cdot9\cdot8}{3\cdot2\cdot1}\\\\\\\dfrac{10!}{3!7!}=10\cdot3\cdot4\\\\\\\boxed{\boxed{\dfrac{10!}{3!7!}=120}}$
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12! / (3!15!)?

Edito com a terceira quando voltar