Problema Solution
Table-tennis balls numbered from 1 to 20 are placed in a box. Three balls are drawn at random. What is the probabibility of drawing 3 numbers less than ten if no replacement occurs?
Answer provided by our tutors
There are 20C3 total possible ways to choose them:
20C3 = 20!/(3!(20 - 3)!) = 20!/(3!17!) = 18*19*20/(2*3) = 1140
To get 3 balls less than 10, there are 9 balls that fit that criterion (that have numbers less than 10), so that gives us a total of 9C3 ways to draw 3 numbers less that 10 or:
9C3 = 9!/(3!(9-3)!) = 7*8*9/(2*3) = 84
P(drawing 3 numbers less than ten) = 9C3/20C3 = 84 / 1140 = 7/95 = 0.0737