Answer:
There are a total of possible 1820 results.
Step-by-step explanation:
Since there are two competitions, one for boys and one for girls, and we want all the possible results we will calculate the possible combinations for the boys and multiply them by the possible combinations for the girls. This is shown below:
[tex]Boys = \frac{15!}{3!(15 - 3)!} = \frac{15!}{3!12!} = \frac{15*14*13*12!}{3!12!}\\Boys = \frac{15*14*13}{3*2*1}\\Boys = \frac{15*14*13}{3*2*1}\\Boys = 455[/tex]
[tex]Girls = \frac{4!}{3!*(4 - 3)!}\\Girls = \frac{4*3!}{3!}\\Girls = 4[/tex]
Total number of possible results:
[tex]results = 4*455\\results = 1820[/tex]
