- Thread starter
- #1

#### Abstract3000

##### New member

- Feb 14, 2014

- 1

I have a question I am trying to figure out how it works and I am so confused I need a break down of what is exactly going on with this problem

the Question.

"Concern three persons who each randomly choose a locker among 12 consecutive lockers"

What is the probability that no two lockers are consecutive?

The answer given that confuses me even more:

-----------------------------------------------------------------------

1st to find ways exactly 2 lockers are consecutive

X X _ _ _ _ _ _ _ _ _ _ 9 Ways

_ X X _ _ _ _ _ _ _ _ _ 8 Ways

_ _ X X _ _ _ _ _ _ _ _ 8 Ways

5 others w/8

_ _ _ _ _ _ _ _ X X _ _ 8

_ _ _ _ _ _ _ _ _ X X _ 8

_ _ _ _ _ _ _ _ _ _ X X 9

# = 9X2 + 9X8 = 90

Next # Ways w/3 consecutive = 10 start in 1,2,....,10

== P(no 2 consec) = 1 - 100/C(12,3) ~ .545 = 5.45X10^10-1

--------------------------------------------------------------------------

This is the teachers solution and I have absolutely no idea on how he got all the number he did I am really lost (on all of it, the solution makes no sense in what he has written down I don't get where he gets the 8's the 9's or the 10 from), anyone understand this and have the time to break it down for me?

Thanks!