The following table lists the $15$ largest U$.$S$.$ universities according to enrollment in a recent year

RANK

UNIVERSITY

STATE

ENROLLMENT

$1$

Texas A&M

TX

$63,813$

$2$

University of Central Florida

FL

$62,953$

$3$

Ohio State University

$OH$

$58,663$

$4$

Arizona State University

AZ

$51\mathrm{.}984$

$5$

The University of Texas

TX

$50,950$

$6$

University of Minnesota

$MN$

$50,678$

$7$

University of Florida

FL

$50,645$

$8$

Michigan State University

$9$

University of Maryland

MD

$50,538$

MI

New York University

NY

$50,248$

$10$

Florida International

$11$

University

FL

$50,027$

$12$

Rutgers University

NJ

$49,428$

IN

$48,514$

$14$

Penn State University

PA

$47,307$

$15$

University of Illinois

$.$

$45,842$

$($Round your answers to $4$ decimal places, eg$.0\mathrm{.}2153.)$

a$.$ If five different universities are selected randomly from the list, what is the probability that exactly two of them have enrollments of more than $50,000?$

enter probability rounded to $4$ decimal places

b$.$ If eight different universities are selected randomly from the list, what is the probability that two or fewer are universities in Flonida? enter probability rounded to $4$ decimal places

c$.$ Suppose universities are being selected randomly from this list with replacement. If six universities are sampled, what is the probability that the sample will contain exactly two universities in Texas? enter probability rounded to $4$ decimal places

$13$

Indiana University

$49,782$

I