Respuesta :
Answer:
165 ways
Step-by-step explanation:
This is the number of combinations of 3 from 11
11C3 = 11! / 3! (11-3)!
= 11*10*9 / 3*2*1
= 165 ways
The combination helps us to know the number of ways an object can be arranged without a particular manner. The number of ways the coach can select 3 of the 11 students is 165.
What is Permutation and Combination?
Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given that there are 11 students on the tennis team. The coach selects 3 of them to go to a tennis clinic.
Now, using the combination the number of ways the coach can select 3 of the 11 students is,
Number of ways = ¹¹C₃
[tex]= \dfrac{11!}{3!(11-3)!}[/tex]
= 165
Hence, the number of ways the coach can select 3 of the 11 students is 165.
Learn more about Permutation and Combination:
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