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

Explanation:

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

Formula for permutation:
`^nP_r=(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=(9!)/((9-3)!)`

`=(9*8*7*6!)/(6!)=504`

Hence, the number of possible orders 504.