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- TL;DR Summary
- Suppose a circular target is divided into three zones bounded by concentric circles of radius 1/3, 1/2, and 1, as illustrated in the following diagram.

If three shots are fired at random at the target, what is the probability that exactly one shot lands in each zone?

My attempt to answer this question: With the radii in the ratio ## 1: \frac12: \frac13 ##, the area of the corresponding circles will be in the ratio of ##1: \frac14: \frac19 ##. The areas of the three rings will be in the ratio of ## \frac34 : \frac{5}{36}: \frac19 ##

So, if three shots are fired at random at the target, the probability that exactly one shots lands in each zone is equal to ## \frac34 \times \frac{5}{36} \times \frac19 = \frac{5}{432}## But author said the answer is ##\frac{5}{432}\times 3! = \frac{5}{72}## How is that?

Would any member of physics forum provide me a satisfactory explanation?