I'm using the Princeton Review online prep course for the GRE and am having trouble understanding their explanation for the following question:
" Two-player tennis teams are selected from the 6 boys and 6 girls in a tennis class.
Quantity A: The total number of possible teams consisting of two girls Quantity B: The total number of possible teams consisting of one boy and one girl.
A Quantity A is greater B Quantity B is greater C The two quantities are equal D The relationship cannot be determined from the information given "
For Quantity A, it would be 6 * 5 / 2! since order does not matter. In their explanation, they say, "The team of Suzette and Tina is not different from the team of Tina and Suzette," which makes sense. However, they say Quantity B is just 6 * 6 - NOT divided by anything because "the choices are from different sources." But this doesn't make sense to me since the team of Suzette and Bob is not different from Bob and Suzette...
Can anyone elaborate on why being from different sources means I don't divide?
Pretend that order did matter. Maybe the team has a captain and a lieutenant.
In A, there are 6 choices for the captain (all 6 girls), then 5 choices for the lieutenant (all 6 girls except for the captain). Total is $6 \cdot 5 = 30$.
In B, there are 6 choices for the captain (all 6 girls), then 6 choices for the lieutenant (all 6 boys). But wait - the captain could have been a boy! So we also have to account for 6 choices for the captain (all 6 boys), then 6 choices for the lieutenant (all 6 girls). Total is $2 \cdot (6 \cdot 6) = 72$.
But order doesn't matter. So for both A and B, we divide the result by $2!$.