Question

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Answer 1

Resposta:

Fatorial ( ! símbolo )

a)

$\frac{15!}{12! \: 3!} \\ \\ \frac{\:15 \times 14 \times 13×\:12! }{12! \: 3 \times 2 \times 1} = \\ \\ 5 \times 7 \times 13 = 455$

b)

$\frac{12! \: 5!}{15!} = \\ \\ \frac{12!\: 5 \times 4 \times 3 \times 2 \times 1}{15 \times 14 \times 13×\:12!} = \\ \\ \frac{ 4 }{7 \times 13} = \frac{4}{91}$

c)

$\frac{12</strong><strong>!</strong><strong>}{9</strong><strong>!</strong><strong>} \\ \\ \frac{12 \times 11 \times 10 \times 9</strong><strong>!</strong><strong>}{9</strong><strong>!</strong><strong>} = \\ \\ 12 \times 11 \times 10 = 1320$

d)

$\frac{150</strong><strong>!</strong><strong>}{148</strong><strong>!</strong><strong>} \\ \\ \frac{150 \times 149 \times 148</strong><strong>!</strong><strong>}{148</strong><strong>!</strong><strong>} =</strong><strong>\\ \\ </strong><strong> 150 \times 14</strong><strong>9</strong><strong> = 22 \: </strong><strong>3</strong><strong>5</strong><strong>0$

e)

$\frac{25</strong><strong>!</strong><strong>}{24</strong><strong>!</strong><strong> + 23</strong><strong>!</strong><strong>} \\ \\ \frac{25 \times 24 \times 23</strong><strong>!</strong><strong>}{24 \times 23</strong><strong>!</strong><strong> \: + 1 \times 23</strong><strong>!</strong><strong> } = </strong><strong>\\ </strong><strong>\\ </strong><strong>\frac{25 \times 24 \times 23!}{</strong><strong>(</strong><strong>24 \: + 1 </strong><strong>)</strong><strong>\times 23! }</strong><strong> \\ </strong><strong> \\ </strong><strong> \frac{25 \times 24 \times 23</strong><strong>!</strong><strong>}{25 \times 23</strong><strong>!</strong><strong>} = </strong><strong>\\ \\ </strong><strong> \frac{24}{1} = 24$

Bons Estudos!