Question

How many 10-person juries can be formed from 27 possible candidates?

Answer 1

The formula for combination is given as

`\begin{gathered} ^nC_r=(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}`

By substitution?

`\begin{gathered} ^nC_r=(n!)/((n-r)!r!) \\ ^nC_r=(n!)/((n-r)!r!) \\ ^(27)C_(10)=(27!)/((27-10)!10!) \\ ^(27)C_(10)=(27!)/((17)!10!) \\ ^(27)C_(10)=(27*26*25*24*23*22*21*20*19*18*17!)/((17!)!10!) \\ ^(27)C_(10)=(3.061359101*10^(13))/(10!) \\ ^(27)C_(10)=(3.061359101*10^(13))/(3628800) \\ ^(27)C_(10)=8436285\text{ } \end{gathered}`

Hence,

8436285 juries of 10 people can be formed from 27 possible candidates