Answer:
210
Step-by-step explanation:
The general formula for picking k items from a total of n is
[tex]_{n}C_{k} = \frac{n! }{(n-k)!k! }[/tex]
Thus, if we want to select a committee of six people from a club with 10 members, the number of combinations is
[tex]_{10}C_{6} = \frac{10! }{(10-6)!6! }[/tex]
[tex]= \frac{10! }{4!6! }[/tex]
[tex]= \frac{10\times9\times8\times7}{4\times3\times2\times1 }[/tex]
[tex]= \frac{5040 }{24 }[/tex]
= 210
The committee can be selected in 210 separate ways.
