Five competitors Amy, Brenda, Carla, Denise and Elise were in a race. How many ways can the podium (top three finishes) look if Amy finishes third?A12B36C67D20
Question
Five competitors Amy, Brenda, Carla, Denise and Elise were in a race. How many ways can the podium (top three finishes) look if Amy finishes third?A12B36C67D20
Solution
The problem is asking for the number of ways the top three finishes can be arranged if Amy is always in the third place.
Step 1: Since Amy is always in the third place, we only need to consider the first and second places.
Step 2: There are 4 remaining competitors (Brenda, Carla, Denise, and Elise) who can take the first place. So, there are 4 possibilities for the first place.
Step 3: After the first place has been taken, there are 3 remaining competitors who can take the second place. So, there are 3 possibilities for the second place.
Step 4: The number of ways the top three finishes can be arranged is the product of the number of possibilities for the first and second places. So, there are 4 * 3 = 12 ways the podium can look if Amy finishes third.
So, the answer is A12.
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