Combinatorics Problem
Probability
Level
2
Fifteen numbers are picked from the set { }. Find the probability that at least three of those numbers are consecutive.
0.1
0.4
0.2
0.5
1.00
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Imagine putting the 15 numbers into seven boxes labelled 123, 456, 789, etc. Each number is put into the box that it helps to label. After all 15 numbers have been distributed among the boxes, some box must have three balls, by the Pigeon-Hole Principle. Thus the probability that some box has three consecutive numbers is 1.