Question

Five balls are chosen from a bag of eight blue balls, six red balls, and five green balls. How many of these five-ball selections contain exactly five red balls?

Answer 1

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?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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:

$C_{6,5} = \frac{6!}{1!5!} = 6$

Hence six of these five-ball selections contain exactly five red balls.

More can be learned about the combination formula at brainly.com/question/25821700

#SPJ1