SOLUTION: Three research department have8,10, and 6 members,respectively.Each department is to select a delegate and an alternate to,represent the department at a conference.In how many ways

Question 1151655: Three research department have8,10, and 6 members,respectively.Each department is to select a delegate and an alternate to,represent the department at a conference.In how many ways can this be done?
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
8 * 8C2 * 10C2 * 6C2 = ways

This comes from:
2*8C2 ways to select two from department A (we count each selection twice for delegate & alternate roles)
times
2*10C2 ways to select two from department B
times
2*6C2 ways to select two from department C
--------
To tutor @ikleyn, I assume it matters. Say A1 goes as delegate and A2 goes as the alternate. If 3 years after the event, someone asks "Who were the delegates sent three years ago?" then their answer will be different for this case than if A2 were the delegate, even though both A1 & A2 were there.

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

I have a question to the tutor @Math_helper:

In this problem, does the order matter ? In other words, is the pair (delegate,alternate) considered as equivalent to the pair (alternate,delegate) and, therefore, counted only once ?

I am asking because I don't know the correct answer for myself.

Thank you.

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