Respuesta :
From the situation described, we have that:
a) The combinations are: {{A1,S1}, {A1,S2}, {A1,S3}, {A2,S1}, {A2,S2}, {A2,S3}, {A3,S1}, {A3,S2}, {A3,S3}, {A4,S1}, {A4,S2}, {A4,S3}}.
b) All the combinations were listed listing each of the art activities with each possible sport activity.
c) Using the Fundamental Counting Theorem, there are 12 combinations.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering that there are 4 art activities and 3 sport activities, the parameters are given as follows:
[tex]n_1 = 4, n_2 = 3[/tex]
Hence the number of combinations is:
N = 4 x 3 = 12.
Then:
a) The combinations are: {{A1,S1}, {A1,S2}, {A1,S3}, {A2,S1}, {A2,S2}, {A2,S3}, {A3,S1}, {A3,S2}, {A3,S3}, {A4,S1}, {A4,S2}, {A4,S3}}.
b) All the combinations were listed listing each of the art activities with each possible sport activity.
c) Using the Fundamental Counting Theorem, there are 12 combinations.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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