Question

Suppose there are 50 possible dancers. How many trios may be formed, assuming the order within a trio does not matter

Answer 1

Answer:

19600 trios may be formed.

Step-by-step explanation:

Since the order of the trios do not matter, we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Groups of three(Trios) from a set of 50. So

$C_{50,3} = \frac{50!}{3!(50-3)!} = 19600$

19600 trios may be formed.