Question 1210159
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There are 50*2 = 100 senators total.
For the first slot we have 100 choices.
For the second slot we have 100-2 = 98 choices. 
We do not have 99 choices since we exclude the second senator from whatever state was chosen as the first slot.
Otherwise, this committee could potentially have two senators from the same state.


We keep this process of subtracting 2 until we account for all five slots.
The five slots have these choices: 100, 98, 96, 94, 92


If order mattered then we would have 100*98*96*94*92 = 8,136,038,400 different committees. 
Roughly 8.136 billion.


However, it appears that none of the seats have a title (such as "chairman" or "treasurer"), so this means a committee like ABCDE is the same as ACBDE. 
Order does <u>not</u> matter.


How many ways are there to scramble the letters in ABCDE? 
There are 5 letters and 5*4*3*2*1 = 120 permutations.
So we must divide that 8.136 billion figure by 120 to arrive at the correct final answer.


8136038400/120 = <font color=red>67800320</font>
When using commas to make the number more readable, it would look like this 67,800,320. This is approximately 67.8 million. 


A bit of random trivia: If you were to form a different committee every second, then it would take about 784.7 days (a little over 2 years) for you to try all 67.8 million options.



Answer: <font color=red>67800320</font>
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