From a bag containing 4 white and 5 black balls a man draws 3 at random; what are the odds against these being all black?
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Solution
The total number of ways in which 3 balls can be drawn is 9C3, and the number of ways of drawing 3 black balls is 5C3; therefore the chance of drawing 3 black balls =5C39C3=5⋅4⋅39⋅8⋅7=542. Thus the odds against the event are 37 to 5.