I'm learning about the multinomial theorem and working 2 examples in a book. I thought I understood the examples until I did example 5c. I don't understand why these two examples are different. In example 5c it says that order is now irrelevant. What do you mean order is irrelevant? Why was the order relevant in 5b? In both examples we are separating into 2 groups of 5... Thank you in advance!!!
EXAMPLE 5b Ten children are to be divided into an A team and a B team of 5 each. The A team will play in one league and the B team in another. How many different divisions are possible?
Solution is 10! / (5! 5! ) = 252
EXAMPLE 5c In order to play a game of basketball, 10 children at a playground divide themselves into two teams of 5 each. How many different divisions are possible?
Solution. Note that this example is different from Example 5b because now the order of the two teams is irrelevant. That is, there is no A and B team, but just a division consisting of 2 groups of 5 each. Hence, the desired answer is
[10! / (5! 5!) ]/2!