Answer:
[tex]1140[/tex]
Step-by-step explanation:
Combinations : If we want to choose [tex]r[/tex] items out of [tex]n[/tex] items, and order of the selection does not matter.
possible ways [tex]=^nc_{r}=\frac{n!}{r!(n-r)!}[/tex]
Total number of students [tex]=20[/tex]
Persons in subcommittee [tex]=3[/tex]
Here order of selection does not matter, so we can use combination to get possible number of ways.
Number of ways [tex]=^{20}c_{3}=\frac{20!}{(20-3)!3!}[/tex]
[tex]=\frac{20!}{17!\times 3!}=\frac{20\times 19\times 18\times 17!}{17!\times 3!}\\\\=\frac{20\times 19\times 18}{6}\\\\=20\times 19\times 3\\\\=1140[/tex]
