First of all, we have to decide the four players out the 6 young people. By definition, the number of subsets of 4 elements from a set of 6 elements is
[tex]\displaystyle \binom{6}{4}[/tex]
Since the order is important, we have to add the fact that each of these subsets can be ordered in 4! ways, leading to a total of
[tex]\displaystyle \binom{6}{4}\cdot 4!=\dfrac{6!}{4!2!}\cdot 4! = \dfrac{6!}{2!}=6\times 5\times 4 \times 3=360[/tex]
Since each game lasts half a hour, it would take 180 hours to play all the possible games
