1. Let S be the set of all outcomes when two dice (one red; one green) are cast. Let E be the subset of outcomes in which both dice are odd, and let F be the subset of outcomes in which both dice are even. How many elements are there in the following sets?

3. According to a New York Times report^{†} on the 16 top-performing restaurant chains, 11 serve breakfast, 11 serve beer, and 10 have full table service. All 16 offered at least one of these services. A total of 5 were classified as "family chains," meaning that they serve breakfast, but do not serve alcohol. Further a total of five serve breakfast and have full table service, while none serve breakfast, beer, and also have full table service.

(a) How many serve beer and breakfast? (b) How many serve beer but not breakfast? (c) How many serve breakfast, but neither have full table service, nor serve beer? (d) How many serve beer and have full table service?

† Source: The New York Times, June 22, 1996, p. 33.

(a) How many possible collections of 4 gums can he pull out?

(b) Harry is fond of combinations of two strawberry and two blackcurrant gums (he feels that the flavors complement each other nicely). How many collections will make Harry happy?

(c) What is the probability that Harry will be happy? (Enter an exact fraction; not a decimal approximation.)

(a) How many different sets of four new members are possible?

(b) How many of those sets of 4 contain both nerds and two computer geeks?

(c) What is the probability that Nico just happens to select both nerds and two computer geeks? (Enter an exact fraction; not a decimal approximation.)

Last Updated:April, 2002

Copyright © 1999 StefanWaner and Steven R. Costenoble

Top of Page