Question 1169916
<font color=black size=3>
There are three slots or seats to fill on this committee.


For the first slot, we have 100 choices since we have 2*50 = 100 senators.
After that person is picked, there are 98 choices left. Why 98 and not 99? Because we cannot pick a senator from the same state as the first person selected.


For example, let's say we pick a senator from Michigan to fill the first seat. The other senator from Michigan cannot be selected if we want this three-person committee to not have two members from the same state.


So again we have 98 choices for the second slot.


Then whoever goes in the second slot will lower the amount of choices down to 96 for similar reasoning as before.


Overall we have 100*98*96 = 940,800 permutations possible 


Since order doesn't matter, we divide by 3! = 3*2*1 = 6 to get (940,800)/6 = 156,800


Note how there are 6 ways to arrange a group of three items
{A,B,C}
{A,C,B}
{B,A,C}
{B,C,A}
{C,A,B}
{C,B,A}
All six sets listed above are the same set since all have A,B,C in some order. The order doesn't matter on a committee. No member outranks another. All that matters is the group overall.


Answer: 156,800
</font>