Question 984391
  
Given:
There are 27+51=78 members of the legislature.
Find the number of ways to choose a 6-member group from the legislature.
 
Solution:
There are 78 choices to choose the first member,
77 choices to choose the second, ...
...
73 choices to choose the sixth member
 
So there is a total of
78*77*76*75*74*73=184933148400 ways to choose.
However, there are 6! ways to arrange among the six members, so the total number of ways to choose 6 members 
=184933148400/6!=256851595 ways.
 
This can also be solved by the combination function,
C(78,6)=78!/((78-6)!6!)
=256851595 ways