Answer:
The number of possible combinations of sports and instrument that Anja can select is 12.
Step-by-step explanation:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!\cdot(n-k)!}[/tex]
It is said that Anja can choose one sport to play and one instrument to learn using the list below:
Sports: softball, basketball, tennis, or swimming
Instruments: guitar, piano, or clarinet.
There 4 options for sports and 3 for an instrument.
Compute the number of ways to select one sport to play as follows:
[tex]n (S)={4\choose 1}=\frac{4!}{1!\cdot(4-1)!}=\frac{4!}{3!}=\frac{4\times3!}{3!}=4[/tex]
Compute the number of ways to select one instrument to learn as follows:
[tex]n(I)={3\choose 1}=\frac{3!}{1!\cdot(3-1)!}=\frac{3!}{2!}=\frac{3\times2!}{2!}=3[/tex]
Compute the number of possible combinations of sports and instrument that Anja can select as follows:
Total number of possible combinations = n (S) × n (I)
[tex]=4\times 3\\=12[/tex]
Thus, the number of possible combinations of sports and instrument that Anja can select is 12.
