#Combinations

Question

1. Number of ways of splitting 10 people into 2 teams of 6 and 4 people respectively. Answer- $^{10}c_{6}$
2. Number of ways of splitting 10 people into 2 teams of 5 people each. Answer – $^{10}c_{5} /2$

Please explain why we divide by 2?

Comments

Because cases repeat in that case.

A B C D E F G H I J

Choosing A B C D E to be our team 1 and rest for team 2 is same as choosing F G H I J to be team 1 and rest for team 2.

This won't happen in first case.