Three brothers enter a race with 8 friends. The racers draw lots to determine their starting positions. What is the probability that the older brother Mike will start in lane 1, with his other brothers, Stan and Steve beside him in lanes 2 and 3, respectively.

Question

anonymous · Answer

Is it 1/99?

barrycarter · Answer

Do you mean 1/990 ?

anonymous · Answer

YES!!!! THANK YOU!!!!! 

I've literally been waiting for over 40 minutes to get an answer. *laughs* Thanks

cruffo · Answer

I know @BagelsAreIcelandic is offline but... maybe @barrycarter could chime in.

I got 2/990.  The order of the two other brothers does not matter.  

So there are 11! different arrangement (sample space)

There are two basic "good" arrangements:

Stan, Steve, Mike, and 8 others  (8! ways for this to happen)
or Stan, Mike, Steve, and 8 others (8! ways for this)

So there are 2 x 8! "good" arrangements.  

Probability = (2 x 8!) / 11! = 2/990

barrycarter · Answer

I think the word "respectively" implies a specific order

cruffo · Answer

Ah...