The formula for combination is given as
[tex]\begin{gathered} ^nC_r=\frac{n!}{(n-r)!r!} \\ \text{where} \\ n=total\text{ number of possible candidates=27} \\ r=Number\text{ of choosing objects from the set=10} \end{gathered}[/tex]By substitution?
[tex]\begin{gathered} ^nC_r=\frac{n!}{(n-r)!r!} \\ ^nC_r=\frac{n!}{(n-r)!r!} \\ ^{27}C_{10}=\frac{27!}{(27-10)!10!} \\ ^{27}C_{10}=\frac{27!}{(17)!10!} \\ ^{27}C_{10}=\frac{27\times26\times25\times24\times23\times22\times21\times20\times19\times18\times17!}{(17!)!10!} \\ ^{27}C_{10}=\frac{3.061359101\times10^{13}}{10!} \\ ^{27}C_{10}=\frac{3.061359101\times10^{13}}{3628800} \\ ^{27}C_{10}=8436285\text{ } \end{gathered}[/tex]Hence,
8436285 juries of 10 people can be formed from 27 possible candidates
