Abox contains 20 different balls numbered from 1 to 20 (different balls have different numbers). at each step, we select a ball uniformly at random, record the number on it, and put it back in the box. this experiment is repeated 10 times. find the probability that all the numbers recorded were distinct.

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answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

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