Answer: 165 combination can be possible.
Step-by-step explanation:
Here, According to the question,
Different types of machines in the weight room in gym = 11
And, . Geoff has time to use only 3 of them this afternoon.
Therefore, total number of different combination of machine can geoff choose from to use
= [tex]11_C_3[/tex]
= [tex]\frac{11!}{3!\times (11-3)! }[/tex] ( because [tex]n_C_r = \frac{n!}{r!(n-r)!}[/tex] )
= [tex]\frac{11!}{3!\times 8! }[/tex]
= [tex]\frac{11\times 10\times 9\times 8!}{6\times 8! }[/tex]
=[tex]\frac{11\times 10\times 9}{6}[/tex]
= [tex]\frac{990}{6}[/tex]
= [tex]165[/tex]
