Question 1101847
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<pre>
The full space of events is the set of all records of the length 9; each the record contains 9 numbers: 

one number from 1 to 365 (the birthday) in each position from 1 to 9. 


The full set contains  {{{365^9}}}  records/elements.



The complement set consists of those records that have no two equal numbers in all 9 positions (no repetition allowed)

    1)  we can select any of               365 numbers in the 1-st position,
    2)  we can select any of the remaining 364 numbers in the 2-nd position,
    . . . 
    and so on . . . till
    . . . 
    8)  we can select any of the remaining 358 numbers in the 8-th position,
    9)  we can select any of the remaining 357 numbers in the 9-th position.


In all, the complementary set has  365*364*363*362*361*360*359*358*357  records/elements.


Therefore, the probability under the question is     {{{1}}} - {{{(365*364*363*362*361*360*359*358*357)/365^9}}} = 0.0946.
</pre>

Also, see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-Combinations.lesson>Elementary Probability problems related to combinations</A>, Problem 7

in this site.