21!
_______ = 162954792
5!·6!·10!
what is are the middle points /interpuncts and exclamation marks for? how was this done?
+33616 The exclamation mark is the factorial sign. So 21!, spoken as twenty-one factorial, means 21*20*19*...*3*2*1,
$$\frac{21!}{5!6!10!}=\frac{21*20*19*...*11*10*9*...*2*1}{5!*6!*10*9*...*2*1}=\frac{21*20*...*11}{5*4*...*2*1*6*5*...*2*1}\\\\=\frac{14079294028800}{120*720}=\frac{14079294028800}{86400}=162954792$$
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+33616 The exclamation mark is the factorial sign. So 21!, spoken as twenty-one factorial, means 21*20*19*...*3*2*1,
$$\frac{21!}{5!6!10!}=\frac{21*20*19*...*11*10*9*...*2*1}{5!*6!*10*9*...*2*1}=\frac{21*20*...*11}{5*4*...*2*1*6*5*...*2*1}\\\\=\frac{14079294028800}{120*720}=\frac{14079294028800}{86400}=162954792$$
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