Colorful Dodgeball Teams
Sixteen people break up into 4 teams of 4 to play dodgeball: Red team, yellow team, green team, and blue team.
How many distinct ways can those 16 players be split up into 4 new teams of 4 such that each team has one member of each color?
The answer is 13824.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Pin the 4 red team members as the first members of new teams (captains maybe). Then each captain choose one color at a time; the combination is 4! = 24. Then they choose the next color; combination is again 24 ways, also for the last color. Thus, 24^3 = 13,824 ways.