Integers 1 through 53 are written on cards, one per card. The stack is thoroughly shuffled. Five cards are drawn. What is the probability that the cards are drawn in their natural order the smallest first, and the rest in increasing order of magnitude?
You have five cards which may have been drawn in any of 120 possible ways. Only one of these is the natural increasing order. The probability of this happening is 1/120.
The specific number of cards is a red herring. Whatever the number you start with, as long as you draw 5 cards there are 5! = 120 variants. Each comes with probability of 1/120.
References
- C. W. Trigg, Mathematical Quickies, Dover, 1985, #91.
Red Herrings: a Sample List
- On the Difference of Areas
- Area of the Union of Two Squares
- Circle through the Incenter
- Circle through the Incenter And Antiparallels
- Circle through the Circumcenter
- Inequality with Logarithms
- Breaking Chocolate Bars
- Circles through the Orthocenter
- 100 Grasshoppers on a Triangular Board
- Simultaneous Diameters in Concurrent Circles
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Copyright © 1996-2012 Alexander Bogomolny
