Respuesta :
In how many ways can a gymnastics team of 4 be chosen from 9 gymnasts?
36
126
3,024
C(9, 4) = 126
Using combination, the number of ways can gymnastics team of 4 be chosen from 9 gymnastics is 126.
What is combination?
A combination is a way of "selecting items from a collection where the order of selection is not matter".
According to the question,
Total number of gymnastics = 9
Number of team need to be selected = 4
In order to find number of ways gymnastics team can be chosen 4 from 9
Combination formula n Cₓ = [tex]\frac{n!}{x!(n-x)!}[/tex]
9C₄= [tex]\frac{9!}{4!(9-4)!}[/tex]
= [tex]\frac{9!}{(5!)(4!)}[/tex]
= [tex]\frac{9.8.7.6.5.4.3.2.1}{(1.2.3.4.5)(1.2.3.4)}[/tex]
= 9.2.7
= 126.
Hence, using combination, the number of ways can gymnastics team of 4 be chosen from 9 gymnastics is 126.
Learn more about combination here
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