Yoma 57B

אלא אמר רבא: נותן שבע למטה לשם פר, וחוזר ונותן אחת למעלה ושבע למטה לשם שעיר.

Rather, Rava said: He presents downward 7 times for the purpose of the bull, and he again presents upward once and downward 7 times for the purpose of the goat.

נתערבו לו כוסות בכוסות ⁠— נותן, וחוזר ונותן,

The Talmud asks another question: What if the cups became mixed, i.e., if the bowl containing the blood of the bull was confused with that of the blood of the goat? The Talmud explains: He presents blood from one cup by sprinkling upward once and downward 7 times, and he again presents a second set of sprinklings from the second cup.

וחוזר ונותן, שלשה פעמים.

And he again presents another set of sprinklings, again from the first cup, which amounts to a total of 3 times. In this manner, he fulfills the obligation no matter which cup was which. If the first cup was that of the bull’s blood and the second was that of the goat, he fulfilled his obligation with the first and second sprinklings. If the first cup contained the blood of the goat, he performed the sprinkling of the goat’s blood before that of the bull, which means his first set of sprinklings are discounted. Consequently, when he sprinkled from the second cup, which contains the bull’s blood, and a third time from the cup of the goat’s blood, he fulfilled his obligation with the second and third sets of sprinklings.

מקצת דמים נתערבו לו, ומקצת דמים לא נתערבו [לו], פשיטא: כי יהיב ⁠— מודאין יהיב.

The Talmud asks yet another question: If only part of the blood became mixed together and part of the blood did not become mixed, e.g., if some of the blood spilled and became mixed in a third vessel, the solution is obvious: When he presents, he presents from the blood of certain identity.