Respuesta :
Using the combination formula, it is found that six of these five-ball selections contain exactly five red balls.
The order in which the balls are selected is not important(as balls A, B, C, D and E is the same outcome as balls B, A, C, D and E), hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.
What is the combination formula?
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, five red balls can be chosen from a set of six, hence the number of selections is the combination of 5 elements from a set of 6, that is calculated from the formula given above:
[tex]C_{6,5} = \frac{6!}{1!5!} = 6[/tex]
Hence six of these five-ball selections contain exactly five red balls.
More can be learned about the combination formula at https://brainly.com/question/25821700
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