Question

find the probability that if 10 different - sized washers are arranged in a row, they will be arranged in order of size. enter your answer as a fraction or round to the first nonzero decimal. p(10 in order of size) =

Explanation:

Step1: Calculate total arrangements

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 10\), so the total number of ways to arrange 10 different - sized washers is \(n!=10! = 10\times9\times8\times7\times6\times5\times4\times3\times2\times1=3628800\).

Step2: Determine favorable arrangements

There are 2 favorable arrangements (either in increasing or decreasing order of size).

Step3: Calculate probability

The probability \(P\) is the number of favorable outcomes divided by the number of total outcomes. So \(P=\frac{2}{10!}=\frac{2}{3628800}=\frac{1}{1814400}\).

Answer:

\(\frac{1}{1814400}\)