tex]...

August 2022 1 9 Report

а) [tex]A \frac{4}{12} - A \frac{4}{11} / A \frac{3}{10}
[/tex]
б) [tex]A \frac{4}{15} + A \frac{5}{14} / A\frac{3}{15}
[/tex]
в) [tex]A \frac{3}{13} / A \frac{3}{15} - A \frac{3}{14} [/tex]

Answers & Comments

eugeke

Verified answer

$A^4_{12}-A^4_{11}:A^3_{10}=11880-7920:720=11880-11=11869\\\\
A^4_{12}= \frac{12!}{(12-4)!}= \frac{12!}{8!}= \frac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8}=9\cdot10\cdot11\cdot12=11880\\\\
A^4_{11}= \frac{11!}{(11-4)!}= \frac{11!}{7!}=7920\\\\
A^3_{10}= \frac{10!}{(10-3)!}= \frac{10!}{7!}=720$

$A^4_{15}+A^5_{14}:A^3_{15}=32760+240240:2730=32760+88=32848\\\\ A^4_{15}= \frac{15!}{(15-4)!}= \frac{15!}{11!}=32760\\\\ A^5_{14}= \frac{14!}{(14-5)!}= \frac{14!}{9!}=240240\\\\ A^3_{15}= \frac{15!}{(15-3)!}= \frac{15!}{12!} =2730$

$A^3_{13}:A^3_{15}-A^3_{14}=1716:2730-2184=\\\\ A^3_{13}= \frac{13!}{10!}=1716 \\\\ A^3_{15}= \frac{15!}{12!}= 2730\\\\ A^3_{14}= \frac{14!}{11!}=2184$

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