Question

fill in the blank 2 points
a person has 10 shirts. how many different ways can they arrange those shirts in a row in their closet? choose your answer...
based on your previous answer, if they hang their ten shirts randomly in the closet, whats the probability that theyre arranged from oldest to newest? (omit commas.)
enter your answer as a fraction.

Explanation:

Step1: Calculate number of arrangements

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

Step2: Calculate probability

There is only 1 correct arrangement (from oldest - to - newest) out of \(10!\) total arrangements. So the probability \(P=\frac{1}{10!}\). Since \(10!=3628800\), the probability is \(\frac{1}{3628800}\).

Answer:

The number of ways to arrange the shirts: 3628800
The probability: \(\frac{1}{3628800}\)