Chapter 0.5, Problem 14E

To determine

whether each situation involves a permutation or a combination and then to find the number of possibilities.

Answer to Problem 14E

The numbers of possibilities are 210possibilities .

Explanation of Solution

Given information :

It is given that to arrange the winner and first, second and third runners-up in a contest with 10 finalists.

In the given event, arrangement does not matter so it is combination

The number of possibilities is given by,

  $\begin{array}{c}C{}_4=\frac{10!}{4!\times \left(10-4\right)!}\\ =\frac{10!}{4!6!}possibilities\\ =\frac{10\times 9\times 8\times 7}{4\times 3\times 2\times 1}possibilities\\ =210possibilities\end{array}$

So, the numbers of possibilities are 210possibilities .