Hazard game

In the Sportka hazard game, 6 numbers out of 49 are drawn. What is the probability that we will win:

a) second prize (we guess 5 numbers correctly)
b) the third prize (we guess 4 numbers correctly)?

Correct result:

p1 =  0.0018 %
p2 =  0.0969 %


C5(6)=(65)=6!5!(65)!=61=6 C1(43)=(431)=43!1!(431)!=431=43 C6(49)=(496)=49!6!(496)!=494847464544654321=13983816 n=49 o=6 s=no=496=43  p1=100 (o5) (s1)(no)=100 6 4313983816=0.0018%
C4(6)=(64)=6!4!(64)!=6521=15 C2(43)=(432)=43!2!(432)!=434221=903 p2=100 (o4) (s2)(no)=100 15 90313983816=0.0969%

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