<PRE><B>Question 1028530</B>
There are 100 P 20 = 1.303995*10^39 different ways to have 20 people pick different numbers (from a pool of 100). No repeated numbers allowed.


Note: 100 P 20 is referring to a &lt;a href=&quot;http://www.regentsprep.org/regents/math/algebra/apr2/lperm.htm&quot;&gt;permutation&lt;/a&gt; 


There are 100^20 = 1*10^40 different ways for 20 people to pick any number they want (repeats are now allowed) 


The probability of 20 people picking different numbers (no repeats) is
(1.303995*10^39)/(1*10^40) = 0.1303995


Subtract this from 100%, which is equivalent to the decimal form 1.00, so


1.00 - 0.1303995 = 0.8696005 which rounds to 0.8696


I&#39;m subtracting from 100% because there are 2 choices
either you have a case where everyone picks different numbers (no repeats)
OR
there is a case where some people pick the same number(s) (repeats allowed). Whether who or how many, it doesn&#39;t matter. 
There are no other possible cases. These two probabilities add to 100%


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Therefore, the final answer is approximately 0.8696 which is approximately 86.96%</PRE>