Respuesta :
Answer:
The number of ways to form different groups of four subjects is 4845.
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!\times (n-k)!}[/tex]
In this case, 4 subjects are randomly selected from a group of 20 subjects.
Compute the number of ways to form different groups of four subjects as follows:
[tex]{n\choose k}=\frac{n!}{k!\times (n-k)!}[/tex]
[tex]{20\choose 4}=\frac{20!}{4!\times (20-4)!}[/tex]
[tex]=\frac{20\times 19\times 18\times 17\times 16!}{4!\times 16!}\\\\=\frac{20\times 19\times 18\times 17}{4\times3\times 2\times 1}\\\\=4845[/tex]
Thus, the number of ways to form different groups of four subjects is 4845.
