Answer :
Answer:
18564 distinct committee of 12 can be formed
In factorial form:
[tex]\frac{18!}{6!12!}[/tex]Explanations:Note that:
[tex]\text{nCr = }\frac{n!}{(n-r)!r!}[/tex]The total number of people, n = 18
The number of people to be selected = 12
The number of distinct committee of 12 people that can be selected from 18 people will be:
[tex]\begin{gathered} 18C12\text{ = }\frac{18!}{(18-12)!12!} \\ 18C12\text{ = }\frac{18!}{6!12!} \\ 18C12\text{ = }\frac{18\times17\times16\times15\times14\times13\times12!}{12!\times6\times5\times4\times3\times2\times1} \\ 18C12\text{ = }\frac{18\times17\times16\times15\times14\times13}{6\times5\times4\times3\times2\times1} \\ 18C12\text{ = }\frac{13366080}{720} \\ 18C12\text{ = }18564 \end{gathered}[/tex]18564 committee of 12 can be formed
This can be written in factorial form as:
[tex]\frac{18!}{6!12!}[/tex]