The probability that A and B share the same birthday is 1/365. The probability that C and D share the same birthday, but on a different date, is (364/365)(1/365). So the probability that A & B share one date and C & D share another is (1/365)(364/365)(1/365). That's one possible combination of shared birthdays, but there are 2 others: A can share with C and B with D, or A can share with D and B with C. Therefore we multiply the above expression by 3 to get:

, or one in 44,530.33.