Respuesta :
Answer:
N = 4 × 3 × 1 = 12 outcomes.
The number of outcomes in the event that Pablo picks one marble of each color N = 12 outcomes
Step-by-step explanation:
Given;
Number of red marbles = 4
Number of green marbles = 3
Number of yellow marbles = 1
The number of outcomes in the event that Pablo picks one marble of each color N;
That means he picks 1 red, 1 green and 1 yellow marble.
N = 4 outcomes for red × 3 outcomes for green × 1 outcome for yellow.
N = 4 × 3 × 1 = 12 outcomes.
The number of outcomes in the event that Pablo picks one marble of each color N = 12 outcomes
Using the combination formula, it is found that there are 12 outcomes in the event that Pablo picks one marble of each color.
The order in which the marbles are picked is not important, hence, the combination formula is used to solve this question.
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, the outcomes are:
- One red marble from a set of 4.
- One green marble from a set of 3.
- One yellow marble from a set of 1.
Hence:
[tex]T = C_{4,1}C_{3,1}C_{1,1} = \frac{4!}{1!3!} \times \frac{3!}{1!2!} \times \frac{1!}{1!0!} = 4 \times 3 \times 1 = 12[/tex]
There are 12 outcomes in the event that Pablo picks one marble of each color.
A similar problem is given at https://brainly.com/question/24437717
