Question

A patient with end-stage kidney disease has nine family members who are potential kidney donors. How many possible orders are there for a best match, a second-best match, and a third-best match?

Answer 1

Answer: 504

Step-by-step explanation:

When we select r things from n things in a order , we use permutations.

Formula for permutation:  $^nP_r=\dfrac{n!}{(n-r)!}$

Given : The number of family members who are potential kidney donors. = 9

Number of people needed to be selected for best match, a second-best match, and a third-best match ( in an order)=3

Then, the number of possible orders are = $^9P_3=\dfrac{9!}{(9-3)!}$

$=\dfrac{9\times8\times7\times6!}{6!}=504$

Hence, the number of possible orders 504.