A jar contains 16 marbles, of which 4 are red, 3 are blue, and the rest are yellow.  If 2 marbles are to be selected at random from the jar, one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?

Each signal that a certain ship can make is comprised of 3 different flags hanging vertically in a particular order.  How many unique signals can be made by using 4 different flags?

The function f is defined by ~$f\left ( x \right )=-\frac{1}{x}$~ for all nonzero numbers x.  If ~$f\left ( a \right )=-\frac{1}{2}$~ and ~$f\left ( ab \right )=\frac{1}{6}$~, then b =

A positive integer n is said to be “prime-saturated” if the product of all the different positive prime factors of n is less than the square root of n.  What is the greatest two-digit prime-saturated integer?

June 25, 1982, fell on a Friday.  On which day of the week did June 25, 1987, fall?  (Note: 1984 was a leap year.)

For any positive integer n, the sum of the first n positive integers equals ~$\frac{n\left ( n+1 \right )}{2}$~.  What is the sum of all the even integers between 99 and 301?

If n = 8¹¹ – 8, what is the units digit of n?

Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y.  At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row.  The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her.  How many such arrangements of the 6 people are possible?

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term.  What is the sum of the 16th, 17th, and 18th terms in the sequence?