Respuesta :

This  would be  6C3

= 6*5*4
----------  =  20 answer
  3*2*1
ajeigbeibraheem

The number of 3 simple random samples that can be selected from a population of size 6 is 20

The combination of an object is the method used in choosing the possible number of arrangements in an array of datasets.

It is can be expressed by  using the formula:

[tex]\mathbf{^nC_r= \dfrac{n!}{r!(n-r)!}}[/tex]

where;

  • [tex]\mathbf{^nC_r}[/tex] =  number of combinations
  • n = total no. of objects in the data set
  • r = no of objects to be chosen in the data set.

From the given information:

  • total no of data n = 6, and;
  • the no of objects to be chosen r = 3

∴

[tex]\mathbf{^nC_r= \dfrac{6!}{3!(6-3)!}}[/tex]

[tex]\mathbf{^nC_r= \dfrac{6!}{3!(3)!}}[/tex]

[tex]\mathbf{^nC_r= \dfrac{6 \times 5 \times 4 \times 3!}{3!(3)!}}[/tex]

[tex]\mathbf{^nC_r= \dfrac{6 \times 5 \times 4}{3\times 2 \times 1}}[/tex]

[tex]\mathbf{^nC_r= 2 \times 5 \times 2}}[/tex]

[tex]\mathbf{^nC_r=20}}[/tex]

Therefore, there are 20 ways to select 3 size random samples from a population of size 6.

Learn more about combination here:

https://brainly.com/question/8018593?referrer=searchResults

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