Permutation and combination

Here's ten balls with number, from 1 to 10.

 

Total of the 10 balls' permutation:

〇〇〇〇〇〇〇〇〇〇

10P10 = 10!.

 

When divided into two each,

〇〇 〇〇 〇〇 〇〇 〇〇

10P2 8P2 6P2 4P2 2P2 = 10!.

 

When divided into three, three, four each,

〇〇〇 〇〇〇 〇〇〇〇

10P3 7P3 4P4 = 10!.

 

Total of the 10 balls' combination:

〇〇〇〇〇〇〇〇〇〇

10C10 = 1.

 

〇〇 〇〇 〇〇 〇〇 〇〇

10C2 8C2 6C2 4C2 2C2 / 5!.

 

〇〇〇 〇〇〇 〇〇〇〇

10C3 7C3 4C4 / 2!.