Chapter 9.6, Problem 39E

To determine

Find the possible number of orders.

Answer to Problem 39E

The possible number of orders is 504

Explanation of Solution

Given:

A patient with end-stage kidney disease has ninefamily members who are potential kidney donors.

There are 9 family members

Only one person from these 9 members is a best match

And another for second best and another for third best match

Thus,to choose 3 persons for first, second and third

This can be done in ${}_9{P}_3$ ways

  ${}_9{P}_3=\frac{9!}{(9-3)!}\left({}_n{P}_r=\frac{n!}{(n-r)!}\right)$

  $\begin{array}{l}=\frac{9\cdot 8\cdot 7\cdot 6!}{6!}\hfill \\ =9\times 8\times 7\hfill \\ =504\hfill \end{array}$

Hence the possible number of orders is 504.