Question

A linguistics professor surveys her class to find out which of the following languages are
spoken in the homes of her 25 students: English, Spanish, and Cherokee. English is spoken
in the homes of all but 1 of the students, and all three languages are spoken in 2 of the
homes. Furthermore, 13 students report that Spanish is spoken at home and 5 report that
Cherokee is spoken at home. Finally, suppose we know that exactly two languages are
spoken in 3 homes (but we don’t know which two languages).

(a) Come up with (and describe clearly) two different scenarios to demonstrate that with-
out additional information, we cannot determine precisely the number of homes in which each combination is languages is spoken.

(b) We can, however, come up with a range of possible values. Specifically, what is the
smallest possible number of homes in which Cherokee is the only language spoken,
given the information above? What is the largest possible number of homes in which
Cherokee is the only language spoken?

Answer 1

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