List the elements in each of the sets. The set \(F\) consisting of the four seasons.

\mathrm{\\{} A t h l e t i c s ~ O f ~ t h e ~ 4,700 students at Medium Suburban College (MSC), 50 play collegiate soccer, 60 play collegiate lacrosse, and 96 play collegiate football. Only 4 students play both collegiate soccer and lacrosse, 6 play collegiate soccer and football, and 16 play collegiate lacrosse and football. No students play all three sports. a. Use the given information to set up a Venn diagram and solve it. HIIIT [See Example 4.] b. Complete the following sentence: \(-\%\) of the college soccer players also play one of the other two sports at the collegiate level.

Rewrite in set notation: He will cater for any event as long as there are no more than 1,000 people, it lasts for at least three hours, and it is within a 50 mile radius of Toronto.

The Honest Lock Company plans to introduce what it refers to as the "true combination lock." The lock will open if the correct set of three numbers from 0 through 39 is entered in any order. a. How many different combinations of three different numbers are possible? b. If it is allowed that a number appear twice (but not three times), how many more possibilities are created? c. If it is allowed that any or all of the numbers may be the same, what is the total number of combinations that will open the lock?

Building Blocks Use a decision algorithm to show that a rectangular solid with dimensions \(m \times n \times r\) can be constructed with \(m \cdot n \cdot r\) cubical \(1 \times 1 \times 1\) blocks. (See the figure.)

A textbook has the following exercise. "Three students from a class of 50 are selected to take part in a play. How many casts are possible?" Comment on this exercise.