Talmud for Berakhot 8:4
בֵּית שַׁמַּאי אוֹמְרִים, מְכַבְּדִין אֶת הַבַּיִת וְאַחַר כָּךְ נוֹטְלִין לַיָּדַיִם. וּבֵית הִלֵּל אוֹמְרִים, נוֹטְלִין לַיָּדַיִם וְאַחַר כָּךְ מְכַבְּדִין אֶת הַבָּיִת:
Beth Shammai say: the house is swept [The place where they ate is swept of crumbs], and then the hands are washed [for grace. For sometimes the waiter is an am ha'aretz and leaves over olive-size food particles; and if you say that the hands are washed first, food will be spoiled. For the waters of this latter washing will drip upon them and "sully" them.] And Beth Hillel say: The hands are washed and then the house is swept. [Beth Hillel hold that it is forbidden to employ a waiter who is an am ha'aretz; and a waiter who is a talmid chacham (a Torah scholar) will not leave over olive-size food particles, but will remove them. And if the water drips upon particles less than the size of an olive, there is no cause for concern. For such particles may be voided to being with. The halachah in this instance is in accordance with Beth Shammai, it being permitted to employ a waiter who is an am ha'aretz.]