There are a hundred competitors at the National Debating Contest, two from each of the 50 US states. In how many ways can five finalists be chosen if no state may have more than one finalist?

GR0001 Jan 5, 2021

#1**+1 **

Any 1 of the 100 can be chosen first

Next.....we can choose any 1 of the other (100 - 2) = 98 ( we can't choose the other one from the first state)

Next.....we can choose any of the remaining (100 - 4) = 96 (we have chosen two from two states and we can't choose the remaining two from either state)...so...we only have 96 to choose from

Continuing with this pattern :

Then.... one from the remaining (100 - 6) = 94

Then... one from the remaining (100 - 8) = 92

So

100 * 98 * 96 * 94 * 92 = 8,136,038,400 ways !!!

THIS IS INCORRECT !!!

CPhill Jan 5, 2021

#2**0 **

Wait, but according to the official national MATHCOUNTS solutions, the answer is 67,800,320 ways, was there something wrong in your solution?

GR0001
Jan 5, 2021

#3**+1 **

Don't know where I made an error....maybe someone else can give you the correct answer....sorry!!!

CPhill
Jan 5, 2021