What is $\frac{27!}{(27 - 11)! 11!}$ $(27!)/((27-11)!11!)$ ?

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What is $\frac{27!}{(27 - 11)! 11!}$ $(27!)/((27-11)!11!)$ ?

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Answer 1 · 2016-03-17T12:50:26

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Explanation:

$\frac{27!}{(27 - 11)! 11!} = \frac{27!}{16! 11!}$ $(27!)/((27-11)!11!)=(27!)/(16!11!)$

$\frac{27!}{16!} \frac{1}{11!}$ $(27!)/(16!)1/(11!)$

$= \frac{27 \times 26 \times 25 \times 24 \times 23 \times 22 \times 21 \times 20 \times 19 \times 18 \times 17}{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}$ $=(color(red)27xx26xx25xxcolor(yellow)24xx23xxcolor(blue)22xx21xx20xx19xx18xx17)/(color(blue)11xx10xxcolor(red)9xx8xx7xxcolor(yellow)6xx5xxcolor(yellow)4xxcolor(red)3xxcolor(blue)2xx1)$

Cancel 27 with $3 \times 9$ $3xx9$
Cancel 22 with $2 \times 11$ $2xx11$
Cancel 24 with $4 \times 6$ $4xx6$

$= \frac{26 \times 25 \times 23 \times 21 \times 20 \times 19 \times 18 \times 17}{10 \times 8 \times 7 \times 5}$ $=(26xx25xx23xx21xx20xx19xx18xx17)/(10xx8xx7xx5)$

$= 26 \times (\frac{25}{5}) \times (\frac{20}{10}) \times 23 \times (\frac{21}{7}) \times 19 \times 18 \times 17 / 8$ $=26xx(25/5)xx(20/10)xx23xx(21/7)xx19xx18xx17//8$

$= 26 \times 5 \times 2 \times 23 \times 3 \times 19 \times 18 \times 17 / 8$ $=26xx5xx2xx23xx3xx19xx18xx17//8$

$= 13, 037, 895$ $=13,037,895$

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What is $\frac{27!}{(27 - 11)! 11!}$ $(27!)/((27-11)!11!)$ ?

1 Answer

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