Math Grouping Help: 20 Students, 4 Groups of 5, Different Schools

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To divide 20 students into 4 groups of 5, the calculation involves choosing groups sequentially: 20C5 for the first group, 15C5 for the second, 10C5 for the third, and 5C5 for the last group. However, the book provides different answers for the grouping and sending groups to schools. For assigning the groups to 4 different schools, the approach simplifies to determining the number of ways to distribute 4 groups into 4 schools, which is a combinatorial problem of placing 4 distinct items into 4 distinct slots. The correct method for both parts of the problem needs clarification, as the initial calculations seem to align with standard combinatorial principles. Understanding these concepts is crucial for accurately solving the problem.
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Homework Statement



Divide 20 students in 4 groups of 5 each. Find the number of ways of doing this?
Also find how can these gropus be sent to 4 different schools?

The Attempt at a Solution



I get both the answers as:
20C5*15C5*10C5*5C5

But my book gives two different answers for the above 2 different question. Help Please!
 
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The first answer looks correct: you first pick 5 out of 20 for the first group, then 5 out of the remaining 15 for the second group, etc.

For the second question, I think you should forget about the students. You have 4 groups, and 4 schools to send them to. In abstract terms: you have 4 balls and 4 slots, how many possible ways are there to put each ball into one slot?
 

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