Question

In a race between 18 people, how many ways can the top 5 finishers be arranged? 1) 1,028,1602) 8,5683) 742,5604) 73,440

Answer 1

Given:

Number of people, n = 18

Let's determine the number of ways the top 5 finishers can be arranged.

Here, we are to use the permutation formula.

Apply the formula:

$^nP_r=\frac{n!}{(n-r)!}$

Where:

n = 18

r = 5

Thus, we have:

$\begin{gathered} ^{18}P_5=\frac{18!}{(18-5)!} \\ \\ ^{18}P_5=\frac{18!}{(13)!} \end{gathered}$

Solving further:

$\begin{gathered} ^{18}P_5=\frac{18\ast17\ast16\ast15\ast14\ast13!}{13!} \\ \\ ^{18}P_5=18\ast17\ast16\ast15\ast14 \\ \\ ^{18}P_5=1028160 \end{gathered}$

Therefore, there are 1,028,160 ways in which the top 5 finishers can be arranged.

ANSWER:

1) 1,028,160