Birthday problem: Difference between revisions
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→{{header|Perl 6}}: Limit to 365.
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For a start, we can show off how to get the exact solution. If we pick n people, the total number of possible arrangements of birthdays is <tt>365<sup>n</sup></tt>. Among those possibilities, there are <tt>C<sup>n</sup><sub>365</sub></tt> where all birthdays are different. For each of these, there are <tt>n!</tt> possible ways to arrange the n people. So the solution is <tt>1 - n!C<sup>n</sup><sub>365</sub>/365<sup>n</sup></tt>, which in Perl 6 can be written:
<lang perl6>say "$_ :", 1 - combinations(365, $_)/365**$_ * [*] 1..$_ for ^
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for 2 ..
printf "%3d people, theory: %.4f, simulation: %.4f\n",
$n, theory($n), simulation(number-of-people => $n);
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