Thread: Confused about combinations

There are 100 members in the U.s. Senate(2 from each state)In how many ways can a committee of 5 senators be formed if no state may be represened more than once.

I think that this a permutation problem but when i re-read it it might be a combination problem

Originally Posted by Rimas

There are 100 members in the U.s. Senate(2 from each state)In how many ways can a committee of 5 senators be formed if no state may be represented more than once.

I think that this a permutation problem but when i re-read it it might be a combination problem

50 senators may form committee in (50*49*48*47*46) / 5! = 2118760 ways.

Knowing that there 100 senators, multiply that number with 2 and you will get total ways of combinations of committee.

Originally Posted by OReilly

50 senators may form committee in (50*49*48*47*46) / 5! = 2118760 ways.

Knowing that there 100 senators, multiply that number with 2 and you will get total ways of combinations of committee.

I don't agree. Let's say there are only 2 states with 2 senators forming a two man comittee.

Senators a and b are from state "whocares"

Senators x and y are from state "Ido"

the combinations with half the senators are:

ax

Multiply that by 2 and you get 2 different combinations, and yet possible combinations are:

ax
ay
bx
by

it's an unfortunate trick of the problem

Originally Posted by Rimas

There are 100 members in the U.s. Senate(2 from each state)In how many ways can a committee of 5 senators be formed if no state may be represened more than once.

There are combin(50,5) to chose the states.
There are 2^5 ways the chose the members.
There are combin(50,5)*2^5 ways to do this: 39200 ways.