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.

Is it 1/8?

Question

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.

Is it 1/8?

anonymous · Answer

The probability that Mike will start in the first lane is 1/8
Now there is only 7 tickets left, the probability that Stan will start in lane 2 is 1/7.
And for Steve 1/6
The probability that all this happens is therefore:
1/8 * 1/7 * 1/6  = 1/336 ~ 0.3%

anonymous · Answer

No, that's not right.

anonymous · Answer

Okey, I think I know why. Wait a second

anonymous · Answer

Alright. :)

anonymous · Answer

Mike has to be first: 1/8
Stan could be either 2 or 3: 1/7 + 1/7 = 2/7
Steve has the be where Stan isn't: 1/6
p = 1/8 * 2/7 * 1/6 = 1/168 ~ 0.6%

Maybe I'm reading the question wrong.