Combinatorics and companion galaxies: Paradox lost

Arp (1994) has presented redshift data for the Local Group of galaxies and for the next major group, whose largest galaxies are M31 and M81, respectively. He observed that the relative redshifts of all 22 of their companions were positive and claimed that the likelihood that this would occur is 1 in 4 x 10(exp 6). We show using the classical combinatoric paradigm of ordered samples (without replacement) that the correct probability for the dominant member of each cluster to possess the lowest observed redshift is approximately 8%.