SOLUTION: The legislature of Puerto Rico consists of a 27-member Senate and a 51-member House of Representatives. How many ways are there to choose a group of six members from the Puerto

Question 984391: The legislature of Puerto Rico consists of a 27-member Senate and a 51-member House of Representatives.
How many ways are there to choose a group of six members from the Puerto Rican legislature?

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

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

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