Let one part be x units long. Let the next part be y-x units long and let the last bit be 6-y units long
when you add these together you get x + (y-x) + (6-y) = 6 units.
Now graph this on a number plane
0 < x < 6
0< y-x < 6
0 < 6-y <6
The area inside this shape represents the total possibility of the stick breaking anywhere. I mean, no matter where the stick is broken it will be represented by a point inside this region.
You want all three bits to be less than 5.
So now you have another smaller regaion to draw,
0 < x < 5
0< y-x < 5
0 < 6-y <5
So the probability that you want is the little area divided by the big area.
Let me know how you go. Maybe take a photo of your graph and post it here.
The 8 boxes are all the same but the 4 balls arn't so the answer will be the same for 4,5,6 or any number more boxes.
The 4 balls can be in one box. 1 way
The are 4 ways to take one ball on it's own. so there are 4 ways to have a 3 to one split.
Say the balls are black, red, green and yellow.
To split them into two piles of 2 balls the black can pair with the red or the black leaving the green and yell ow together, OR
the black can pair with the green, OR the black can pair with the Yellow. 3 ways
So there is a total of 8 ways.
Before I start I will make it very clear that I have not looked at question or answer properly.
I will also say that I have NEVER said it is ok to post AoPS questions, especially when you are just looking for the answer.
Why do I think you are just after the answer?
Becasue you did not notice that originally key elements of the questin were missing.
AND more importantly
Because you just told CPhill his long answer was 'wrong'
It is easy to have a fundamentally correct answer but due to some small error somewhere the last line could be incorrect.
Did you look at CPhill's working? Or did you just plug in the last line and dismiss all he had done for you.
I never saw a thankyou anywhere. (for his time and effort)
Nor did I see you ask for any clarification of his working.
Alan's answer isn't wrong.
Even if there is some small error the working is very detailed and solid.
Which bit don't you understand?
I have opened the earlier question so you can answer there is you want to.
Make sure you also post a link on this thread if you continue this elsewhere.