What is (27!)/((27-11)!11!)27!(2711)!11!?

1 Answer
Mar 17, 2016

13037895

Explanation:

(27!)/((27-11)!11!)=(27!)/(16!11!)27!(2711)!11!=27!16!11!

(27!)/(16!)1/(11!)27!16!111!

=(color(red)27xx26xx25xxcolor(yellow)24xx23xxcolor(blue)22xx21xx20xx19xx18xx17)/(color(blue)11xx10xxcolor(red)9xx8xx7xxcolor(yellow)6xx5xxcolor(yellow)4xxcolor(red)3xxcolor(blue)2xx1)=27×26×25×24×23×22×21×20×19×18×1711×10×9×8×7×6×5×4×3×2×1

Cancel 27 with 3xx93×9
Cancel 22 with 2xx112×11
Cancel 24 with 4xx64×6

=(26xx25xx23xx21xx20xx19xx18xx17)/(10xx8xx7xx5)=26×25×23×21×20×19×18×1710×8×7×5

=26xx(25/5)xx(20/10)xx23xx(21/7)xx19xx18xx17//8=26×(255)×(2010)×23×(217)×19×18×17/8

=26xx5xx2xx23xx3xx19xx18xx17//8=26×5×2×23×3×19×18×17/8

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