How do you simplify (19!)/(13!)?

1 Answer
Oct 1, 2016

19,530,040

Explanation:

! reads as "factorial" It means multiply as shown in the example:

6! = 6xx5xx4xx3xx2xx1 = 720

Because the numbers become so very big, you ideally need a scientific calculator.

However, there is some simplifying you can do ..
(19!)/(13!) = (19xx18xx.......xx14xx(color(red)(13 xx ..... xx1)))/color(red)((13xx12xx11...xx1))

13! forms part of 19! as shown above, so these factors cancel....

(19!)/(13!) = (19xx18xx.......xx14xxcancel(color(red)(13 xx ..... xx1)))/cancelcolor(red)((13xx12xx11...xx1))

leaving only 19xx18xx17xx16xx15xx14 to calculate, which gives

19,530,040" "larr still a horribly big number!