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Practice
Contest

EXPLANATION

It's obvious that we can solve the problem for each compartment separately. Let's find the number of free places in a particular compartment, say Y. If Y> X then our group of friends can't be placed in this compartment. In the other case the number of ways to choose any X places out of given Y should be added to the answer -- in other words, the number of X-combinations of Y elements should be added. This number (let's call it C(Y,X)) can be calculated in many ways:

• using the formula C(Y,X) = Y! / ( X! * (Y-X)! ),
  
• using the relation C(Y,X) = C(Y-1,X) + C(Y-1,X-1),
  
• or even calculating all the required values by hand (both X and Y are very small).
  

SETTER'S SOLUTION

Can be found here

TESTER'S SOLUTION

Can be found here