Hey guys! and
BunuelI'm having trouble here with the interpretation of this question.
So, they're forming a task force that has 1 member of A, 1 member of B, 1 member of C, 2 members of D.
So total possible combinations = 10*10*10*20*19, and we have to consider if the order matters.
I saw multiple resolutions here considering that the order among A, B, and C does matter, while the order between D1 (1st D member) and D2 (2nd D member) doesn't; however since we're talking about a task force of People, the order, in my opinion, doesn't matter for all of the taskforce (A,B,C,D1 and D2).
Let's think of a case in which, for group A, Ana was selected.
For group B, Barbara was selected.
For group C, Carlos was selected
And for group D, Daniel and Donald were selected.
Alright, so we have the following task force: Ana, Barbara, Carlos, Daniel, and Donald.
And in my conception, it would be the same task force if we write: Barbara, Carlos, Ana, Donald and Daniel (just changed the order, but still the exact same people)
Thus, the order doesn't matter at all for the whole task force.
Thus, the solution of the problem must be (A*B*C*D*D-1)/6! = (10*10*10*20*19)/ 6! = 19000/36
What am I missing here? Why does the order among A, B, and C groups matter?
Thanks!