Question 192089: Here is a problem that I sent into my math teacher, but I got it back incorrect. I'm not sure what I did wrong!
There are 100 members of the senate, 2 from each state. In how many ways can a committee of 5 senators be formed if no state can be represented more than once?
I tried to logic this out in my head, and my answer was:
There are five chairs. The first chair has 50 options (not 100, since the states can only be represented once), then the second chair has 49 options, 48 for the third, 47, and 46.
50x49x48x47x46=254,251,200
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There are 100 members of the senate, 2 from each state. In how many ways can a committee of 5 senators be formed if no state can be represented more than once?
I tried to logic this out in my head, and my answer was:
There are five chairs. The first chair has 50 options (not 100, since the states can only be represented once), then the second chair has 49 options, 48 for the third, 47, and 46.
50x49x48x47x46=254,251,200
---
That gives you the number of arrangements of the
5 one they are selected, but you want the number of groups
of size 5.
--------------------------------------
# of ways to select 5 states: 50C5 = 2,118,760
# of ways to pick one of each pair from the 5 states: 2^5 = 32
--------------------------------------------------------------
Final answer: (50C2)*2^5 = 67,800,320
==============================================
Cheers,
Stan H.
|
|
|
