Re: Probabilities of drawing certain cards

just for fun and cool uses for Perl, here the math for the first column

  DB<29> $h = 5

  DB<30> sub A_and_B { bk($n-2,$h-2) / bk($n,$h) }

  DB<31> sub bk { my ($n,$k) = @_; fac($n)/(fac($k)*fac($n-$k)) }

  DB<32> sub fac { my ($n) =@_; my $f=1; $f*=$_ for 2..$n; $f}

  DB<33> printf ( "%i %0.3f\n", $n=$_, A_and_B ) for 6..15
6 0.667
7 0.476
8 0.357
9 0.278
10 0.222
11 0.182
12 0.152
13 0.128
14 0.110
15 0.095
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remaining cols left for the interested reader. :) °

update

°) spoiler

  DB<74> sub A_and_B { bk($n-2,$h-2) / bk($n,$h) }

  DB<75> sub A_and_not_B { bk($n-2,$h-1) / bk($n,$h) }

  DB<76> sub A_xor_B { 2*bk($n-2,$h-1) / bk($n,$h) }                  
+    # NB: 2 * A_and_not_B

  DB<77> sub A_or_B { ( 2*bk($n-2,$h-1) + bk($n-2,$h-2) ) / bk($n,$h) 
+}   # NB: A_and_B + A_xor_B 

  DB<78> printf ( "%2i ".("\t%2.1f"x4)."\n", $n=$_, map {100*$_} A_and
+_B, A_and_not_B, A_xor_B, A_or_B ) for 6..15
 6      66.7    16.7    33.3    100.0
 7      47.6    23.8    47.6    95.2
 8      35.7    26.8    53.6    89.3
 9      27.8    27.8    55.6    83.3
10      22.2    27.8    55.6    77.8
11      18.2    27.3    54.5    72.7
12      15.2    26.5    53.0    68.2
13      12.8    25.6    51.3    64.1
14      11.0    24.7    49.5    60.4
15      9.5     23.8    47.6    57.1

  DB<79>
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