SOLUTION: Congratulations! You have just won 25 video game tokens to use on these three challenging arcade gamse: Mighty Mediecal Monsters, Radical Racing Robots and Adventures Around the Am

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Question 2202: Congratulations! You have just won 25 video game tokens to use on these three challenging arcade gamse: Mighty Mediecal Monsters, Radical Racing Robots and Adventures Around the Amazon. All you have to do to collect your prize is answer this question: How many different ways are there to spend your 25 tokens on these three games provided that you play each game at least once?
Answer by khwang(438) (Show Source):
You can put this solution on YOUR website!
Assume all the 25 tokens are the same, the three games use 25 tokens
without caring the order as repeating combinations 3 different objects
25 times.
Just like the number of positive integer solutions of the equation
X + Y + Z = 25
Or equivalently
X-1 + Y-1 + Z-1 = 22.
Since X-1 >=0, Y-1>=0,and Z-1>=0(means each game at least once)
There are H(3,22) = C(3+22-1,22) = C(24,22) = 24*23/2 = 276...Answer