Nine people are entered in a race. If there are no ties, in how many ways can the first three places be awarded?
3
252
472
504
How many choices for the first place? 9
How many choices for the second place? 8
(because there are only 8 people left after the first place)
How many choices for the third place? 7
How many ways altogether? use the multiplication rule.
504?
yep! That's correct!
The number of ways to award the first three places in a race can be found using the concept of permutations.
To determine the number of ways to award the first place, you have nine participants to choose from. After selecting one person, there are eight remaining possibilities for the second place. Finally, for the third place, there are seven possible choices remaining. The number of ways to award the first three places is the product of these numbers: 9 * 8 * 7 = 504.
Therefore, the correct answer is 504.