Question

Three more dogs enter the race. Now there are 6 dogs in the race, with prizes for 1st, 2nd, and 3rd place. In how many ways can the 3 prizes be awarded to 6 dogs?

a. 120
b. 90
c. 60
d. 30

Answer 1

There are 120 ways to award prizes for 1st, 2nd, and 3rd places among 6 dogs in a race. This is because there are 6 choices for 1st place, then 5 choices for 2nd, and finally 4 choices for 3rd, multiplied together.

Step-by-step explanation:

To determine the number of ways prizes can be awarded to 6 dogs for 1st, 2nd, and 3rd places, we use the concept of permutations. In essence, we are looking for the number of different orders in which 3 dogs can be chosen from a group of 6 to fill the 3 prize positions.

For the 1st place prize, we have 6 possible choices (since there are 6 dogs). After awarding the 1st place, we have only 5 dogs left for the 2nd place prize. Similarly, for the 3rd place prize, we would have 4 remaining dogs to choose from. This is a permutation problem because order matters: the arrangement of dogs in 1st, 2nd, and 3rd places is significant.

So, the number of different permutations is calculated by multiplying the number of choices for each position:

6 (choices for 1st) × 5 (choices for 2nd) × 4 (choices for 3rd) = 120 ways.

Therefore, the correct answer is (a) 120.