The following table lists the 25 largest U.S. universities according to enrollment figures from The World Almanac. The state of location is given in parentheses.

University Enrollment

University of Phoenix (AZ) ...........160,150

Ohio State University (OH) ........... 51,818

Arizona State University (AZ) .......... 51,234

University of Florida (FL) ............. 50,822

University of Minnesota (MN) ........... 50,402

University of Texas at Austin (TX) ........ 49,697

University of Central Florida (FL) ......... 46,719

Michigan State University (MI) .......... 45,520

Texas A&M University (TX) ........... 45,380

University of South Florida (FL) ......... 43,636

Penn State University Park (PA) .......... 42,914

University of Illinois (IL) ............ 42,728

University of Wisconsin (WI) ........... 41,466

New York University (NY) ........... 40,870

University of Michigan (MI) ............ 40,025

Florida State University (FL) ........... 39,973

University of Washington (WA) ......... 39,524

Purdue University (IN) .............. 39,228

Indiana University (IN) .............. 38,247

University of California, Los Angeles (CA) ....... 38,218

Florida International University (FL) ........ 37,997

University of Arizona (AZ) ........... 36,805

California State University, Fullerton (CA) ..... 35,921

California State University, Long Beach (CA) ..... 35,574

University of Maryland, College Park (MD) ..... 35,300

a. If five different universities are selected randomly from the list, what is the probability that three of them have enrollments of 40,000 or more?

b. If eight different universities are selected randomly from the list, what is the probability that two or fewer are universities in Florida?

c. Suppose universities are being selected randomly from this list with replacement. If five universities are sampled, what is the probability that the sample will contain exactly two universities in California?