Question

Alguém me ajuda por favor

Answer 1

a) $\dfrac{8!}{6!}$

$=\dfrac{8\cdot 7 \cdot \diagup\!\!\!\!\! 6!}{\diagup\!\!\!\!\! 6!}\\ \\ =8 \cdot 7\\ \\ =56$


b) $\dfrac{9!}{10!}$

$=\dfrac{\diagup\!\!\!\!\! 9!}{10\cdot \diagup\!\!\!\!\! 9!}\\ \\ =\dfrac{1}{10}$


c) $\dfrac{3!}{4!}+\dfrac{4!}{5!}$

$=\dfrac{\diagup\!\!\!\!\! 3!}{4\cdot \diagup\!\!\!\!\! 3!}+\dfrac{\diagup\!\!\!\!\! 4!}{5\cdot \diagup\!\!\!\!\! 4!}\\ \\ =\dfrac{1}{4}+\dfrac{1}{5}\\ \\ =\dfrac{5+4}{20}\\ \\ =\dfrac{9}{20}$


d) $\dfrac{7!}{5! \cdot 2!}$

$=\dfrac{7\cdot 6 \cdot \diagup\!\!\!\!\! 5!}{\diagup\!\!\!\!\! 5! \cdot 2 \cdot 1}\\ \\ =\dfrac{42}{2}\\ \\ =21$


e) $\dfrac{20!}{18!\cdot 2!}$

$=\dfrac{20\cdot 19 \cdot \diagup\!\!\!\!\!\! 18!}{\diagup\!\!\!\!\!\! 18!\cdot 2\cdot 1}\\ \\ =\dfrac{20\cdot 19}{2}\\ \\ =\dfrac{380}{2}\\ \\ =190$