Adam Clarke on Exodus 12:3

In the tenth day of this month - In after times they began their preparation on the thirteenth day or day before the Passover, which was not celebrated till the fourteenth day, see Exo 12:6 : but on the present occasion, as this was their first passover, they probably required more time to get ready in; as a state of very great confusion must have prevailed at this time. Mr. Ainsworth remarks that on this day the Israelites did afterwards go through Jordan into the land of Canaan; Jos 4:19. And Christ, our Paschal Lamb, on this day entered Jerusalem, riding on an ass; the people bearing palm branches, and crying, Hosanna, Joh 12:1, Joh 12:12, Joh 12:13, etc.: and in him this type was truly fulfilled.

A lamb - The original word שה seh signifies the young of sheep and of goats, and may be indifferently translated either lamb or kid. See Exo 12:5.

A lamb for a house - The whole host of Israel was divided into twelve tribes, these tribes into families, the families into houses, and the houses into particular persons; Numbers 1, Jos 7:14 - Ainsworth.