Question

18. There are 44 runners in a race, and no ties. In how many ways can the first three finishers be chosen from the 44 runners, regardless of how they are arranged?

Answer 1

Since the total number of runners is 44

Since we need to choose the first 3

Then we will use the combination

$^{44}C_3=\frac{44\times43\times42}{3\times2\times1}$

Simplify it to get the answer

$^{44}C_3=44\times43\times7=13244$

There are 13244 ways to choose them