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.

Tyra Banks is choosing three of the remaining nine contestants in the running to be America’s Next Top Model to appear in Cover Girl Magazine. 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.