Chapter 0.5, Problem 17E

To determine

the ways can the manager choose the top 4 spots.

Answer to Problem 17E

The numbers of possibilities are 45possibilities .

Explanation of Solution

Given information :

It is given that the manager of a softball team has 7 possible players in mind for the top 4 spots in the lineup.

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

The number of possibilities is given by,

  $\begin{array}{c}C{}_4=\frac{7!}{4!\times 3!}\\ =\frac{7\times 6\times 5\times 4\times 3\times 2}{4\times 3\times 2\times 3\times 2}possibilities\\ =\frac{7\times 5}{1}possibilities\\ =35possibilities\end{array}$

So, the numbers of possibilities are 35possibilities .