<PRE><B>Question 1122845</B>
&lt;br&gt;
Each senator can vote either of 2 ways.&lt;br&gt;
The number of different ways the 100 senators can vote is 2^100.&lt;br&gt;
That total number of ways, 2^100, is equal to&lt;br&gt;
100C0 + 100C1 + 100C2 + ... + 100C99 + 100C100&lt;br&gt;
The only way not to get a majority (one way or the other) is if the vote is 50-50.  The number of ways that can happen is 100C50.&lt;br&gt;
So the number of ways to get a majority (one way or the other) is then&lt;br&gt;
2^100 - 100C50&lt;br&gt;
If you mean the number of ways of getting a majority &quot;yes&quot; votes, it is&lt;br&gt;
(2^100 - 100C50)/2</PRE>