[Avodah] Is it better to have one person do a vadai mitzvah

[L Reich]

Chans Luntz posted a learned message re. 

"...........Mishna there (Yevamos 98b) is discussing a case where five women
give birth to sons together in one place and the sons all get mixed up,
so nobody knows which son belongs to which mother (and hence to which
father) but where each of the mothers also have a vadai son of the same
father as the one that got mixed up.  And the five mixed up sons grow up
and marry and each die childless.  So what the Mishna prescribes if that
for the first woman, four of the vadai sons give her chalitza, and the
last of the sons marries her - on the basis that, if she is in fact his
brother's wife, he will be doing yibum, and if not, well her real yavam
gave her chalitza as one of the four, and she is free to marry.  And
then the same procedure is repeated for the second woman, with a
different one of the vadai sons taking her in marriage, and so for all
five..........."

Others have added to the discussion, prompting me to pull out some notes
which I compiled many, many years ago following my amateurish mathematical examination.

I stand to be corrected if I erred, but my findings were that if each man  performed
one Yibum there were 120 possible outcomes as follows:-

5     Yibumim      1     possibility
3     Yibumim    10     possiblities
2     Yibumim    19     possibilites
1      Yibum       46     possibilities
0     Yibumim     44     possibilities

We see that out of the 120 there are 76 cases (120-44), i.e a 63%+ possibility that will be at least one Yibum and 30 cases (1 + 10 +19), i.e. a 25% possibilty that there be more than one.

Elozor Reich, Manchester

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