At the American Kennel Club, there are 36 dogs entered in a show where there will be a first-, second-, and third- place award. How many possibilities are there for these awards?
what is 36x35x34 ?
Do you know why ?
To determine the number of possibilities for the awards, you need to use the concept of permutations.
In this scenario, the first-place award can go to any of the 36 dogs, the second-place award can go to any of the remaining 35 dogs, and the third-place award can go to any of the remaining 34 dogs.
To calculate the total number of possibilities, you need to multiply the number of choices for each award. Using the multiplication principle, the total number of possibilities is:
36 * 35 * 34 = 42,840
Therefore, there are 42,840 possibilities for the first-, second-, and third-place awards at the American Kennel Club dog show.