Question 382163
5 wooden blocks numbered 1,2,3,4,5 are placed  by a young child in a row. What is the probability that the numbered formed is...
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First we will calculate the denominator of the probability for it is the same for both problems.

It is the number of ways to pick 5 things from 5 things and position them. 

Thats "5 Position 5" or 5P5 = {{{5!/(5-5)!= 5!/0! = 120/1=120}}} 
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1. Less than 20,000?
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We must choose the first digit to be 1. Then we have to pick 4 of the
remaining 4 digits and position them

That's "4 position 4" or {{{4!/(4-4)!= 4!/0! = 24/1=24}}}

So the probability is 24 out of 120 or {{{24/120 = 1/5}}}

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2. More than 40,000?
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We must choose the first digit as 4 or 5.  That's 2 ways to pick the
first digit. For each of those 2 ways to pick the first digit, we have 
to pick 4 of the remaining 4 things and position them. So there are 

2*(4P4) = {{{2*(4!/(4-4)!)= 2(4!/0!) = 2(24/1)=2(24)=48}}}

So the probability is 48 out of 120 or {{{48/120 = 2/5}}}

Edwin</pre>