Chapter 9.1, Problem 4E

Solution

To state: The numbers of ways in which five ribbons for the first place through fifth place can be awarded to the top 5 dogs in a show.

The resultant answer is 120 ways.

Given information:

Five ribbons for the first place through fifth place have to be awarded to the top 5 dogs in a show.

Explanation:

Number of ribbons is 5 and number of dogs is 5.

Any of the 5 dogs can be awarded the first ribbon. Thus there are 5 ways in which first ribbon can be awarded.

Now 4 ribbons and 4 dogs are remaining, the second ribbon can be awarded to any of the 4 dogs in 4 ways.

Now 3 ribbons and 3 dogs are remaining, the second ribbon can be awarded to any of the 3 dogs in 3 ways.

Now 2 ribbons and 2 dogs are remaining, the second ribbon can be awarded to any of the 2 dogs in 2 ways.

At last there is 1 ribbon and 1 dog is remaining it can be can be awarded in 1 way.

The number of ways is:

  $5\cdot 4\cdot 3\cdot 2\cdot 1=120$

Therefore, there are 120 ways in which five ribbons for the first place through fifth place can be awarded to the top 5 dogs in a show.