Chapter 6.2, Problem 6MRPS

Solution

To find: The possible number of different course selections.

86493225 different course selections are possible.

Given:

18 courses must be selected from 30 courses.

Calculation:

Here, the order of selecting the courses is immaterial.

So, finding the number of possible course selections involves combinations.

Now, the number of ways of selecting 18 courses from 30 courses is,

  $\begin{array}{c}C{}_{18}=\frac{30!}{\left(30-18\right)!18!}\\ =\frac{30\cdot 29\cdot 28\cdot 27\cdot 26\cdot 25\cdot 24\cdot 23\cdot 22\cdot 21\cdot 20\cdot 19\cdot \cancel{18!}}{12!\cancel{18!}}\\ =86493225\end{array}$

Hence, 86493225 different course selections are possible.