Question

Evaluate the following expression: 20!/(13!(20-13)!)

Factors and multiples
ANSWERED
asked 2021-08-10
Evaluate the following expression:
\(\displaystyle{20}\frac{!}{{{13}!{\left({20}-{13}\right)}!}}\)

Answers (1)

2021-08-11
\(\displaystyle{20}\frac{!}{{{13}!{\left({20}-{13}\right)}!}}={20}\frac{!}{{{13}!{7}!}}\)
\(\displaystyle\frac{{{20}\times{19}\times{18}\times{17}\times{16}\times{15}\times{14}\times{13}!}}{{{13}!{7}!}}\)
\(\displaystyle=\frac{{{20}\times{19}\times{18}\times{17}\times{16}\times{15}\times{14}}}{{{7}\times{6}\times{5}\times{4}\times{3}\times{2}\times{1}}}\)
\(\displaystyle=\frac{{{20}\times{19}\times{18}\times{17}\times{16}\times{15}\times{14}}}{{{\left({7}\times{2}\right)}{\left({5}\times{4}\right)}{\left({6}\times{3}\right)}}}\)
\(\displaystyle=\frac{{{20}\times{19}\times{18}\times{17}\times{16}\times{15}\times{14}}}{{{14}\times{20}\times{18}}}\)
\(\displaystyle={19}\times{18}\times{16}\times{15}\)
=77520
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