Question

8) Calcule:
a) A10,3 =
b) A6,2 - A5,3 =
c) A28,2 . A10,4 =​

Answer 1

Resposta: a) 720, b) - 30, c) 3810240.

Lembre-se que a fórmula do calculo de arranjo simples é:

$A_{p,q}=\dfrac{p!}{(p-q)!}$

Onde Ap,q lê-se ''arranjo de p elementos tomados de q em q''.

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a) A10,3

$A_{10,3}=\dfrac{10!}{(10-3)!}$

$A_{10,3}=\dfrac{10!}{7!}$

$A_{10,3}=\dfrac{10\times9\times8\times7!}{7!}$

$A_{10,3}=10\times9\times8$

$A_{10,3}=720$

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b) A6,2 – A5,3

$A_{6,2}-A_{5,3}=\dfrac{6!}{(6-2)!}-\dfrac{5!}{(5-3)!}$

$A_{6,2}-A_{5,3}=\dfrac{6!}{4!}-\dfrac{5!}{2!}$

$A_{6,2}-A_{5,3}=\dfrac{6\times5\times4!}{4!}-\dfrac{5\times4\times3\times2!}{2!}$

$A_{6,2}-A_{5,3}=6\times5-5\times4\times3$

$A_{6,2}-A_{5,3}=30-60$

$A_{6,2}-A_{5,3}=-\,30$

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c) A28,2 × A10,4

$A_{28,2}\times A_{10,4}=\dfrac{28!}{(28-2)!}\times\dfrac{10!}{(10-4)!}$

$A_{28,2}\times A_{10,4}=\dfrac{28!}{26!}\times\dfrac{10!}{6!}$

$A_{28,2}\times A_{10,4}=\dfrac{28\times27\times26!}{26!}\times\dfrac{10\times9\times8\times7\times6!}{6!}$

$A_{28,2}\times A_{10,4}=756\times504$

$A_{28,2}\times A_{10,4}=3810240$

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Bons estudos e um forte abraço. — lordCzarnian9635.