Recall that in Section 1.1 we introduced the following arrangement of numbers, which is ca...

Recall that in Section 1.1 we introduced the following arrangement of numbers, which is called Pascal’s triangle.

Notice that the fourth line* of this triangle contains the numbers 1, 4, 6, 4, 1, which, as we saw in Example are precisely the counts of the number of subsets of a four-element set with 0, 1, 2, 3, and 4 elements, respectively.

Donald Trump has 10 contestants left on The Apprentice and wishes to consider four of them as potential project managers for the next task. In how many ways can this be done? (Hint: Use Pascal’s triangle as you did in Exercises.)

Example Finding All Subsets of a Set Systematically Find all subsets of the set {1, 2, 3, 4}.

We can organize this problem by considering subsets according to their size, going from 0 to 4. This method is illustrated in the following table.