Question

In order to conduct an experiment, 4 subjects are randomly selected from a group of 20 subjects. How many different groups of four subjects are possible?

Answer 1

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:

${n\choose k}=\frac{n!}{k!\times (n-k)!}$

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:

${n\choose k}=\frac{n!}{k!\times (n-k)!}$

${20\choose 4}=\frac{20!}{4!\times (20-4)!}$

      $=\frac{20\times 19\times 18\times 17\times 16!}{4!\times 16!}\\\\=\frac{20\times 19\times 18\times 17}{4\times3\times 2\times 1}\\\\=4845$

Thus, the number of ways to form different groups of four subjects is 4845.