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Arrangement of Washers Find the probability that if 5 different-sized washers are arranged in a row, they will be arranged in order of size.

$\dfrac{1}{60}$

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 5

Sampling and Data

Probability Topics

Temple University

Cairn University

University of St. Thomas

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Now we have five washers and different sizes. And, um, we want to know if we randomly arrange these washers. What is the probability that they appearing order? So we want to know the probability that they are in order. And the Sequels, the number of ways and thio make the main order divided by the total number of ways to arrange them. And so assume that the order here refers to ascending order. And obviously there is only one way Thio make thes washers in order. Right? And so the only problem we have is to find the denominator. And to do that, we need to recall the definition of permutation. And if we select our objects out of and and we want to know how many ways we could sort these are objects we need to use this notation NPR Andi, this can be computed as and factorial divided by n minus r factorial. And in our problem, we want to select five washes out of five and sort them so the denominator equals five p five. This equals five sorry. Five factorial divided by zero factorial Note that zero factorial equals one rather than zero. So this goes to 120 Andi. Finally, the probability that they're in order equals one divided by 120. Which goes to point Yeah. 08 and we're done.

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