Question

10. There are seven gymnasts at a competition: Amanda, Dorothy, Gabby, Jacquelyn, Kelly, Madison, and Simone. One is chosen for the gold medal, one for silver, and one for bronze. What are the number of possibilities for the winning gold, silver, and number of ordered k-element subsets of a set S with n elements. What is the set S? What are k and n?

Answer 1

There are seven gymnasts. So possibility for gold is among seven. Possibility for silver remains now six and possibilities for bronze among remaining five gymnasts. It is a case of combination selection of three member from seven members.Set S is the set of seven gymnasts i.e n is 7. And k is 3.

Now number of ordered k-element subset =ⁿ​​​​​​C_​k

=⁷C₃

=35.