There are 6 contestants in a singing competition. How many different ways can first, second, and third place be awarded?
There are 6 contestants from whom to choose the first place, 5 remaining the second, and 4 the third. Since they are independent events, we multiply them together to get the number of ways.
in a writting competition, the first place winner receives 1/2 of the prize money.the second runner up receives 1/4 of what the winner won .what was the total amount of prize money distributed if the winner receives $6000.
To find the number of different ways that first, second, and third place can be awarded in a singing competition with 6 contestants, we can use the concept of permutations.
To explain how to get the answer, let's break it down step by step:
Step 1: Determine the number of contestants who can win first place.
In this case, all 6 contestants are eligible for first place, so there are 6 possibilities.
Step 2: Determine the number of remaining contestants who can win second place.
Since one contestant has already won first place, there are 5 remaining contestants who are eligible for second place.
Step 3: Determine the number of remaining contestants who can win third place.
Since one contestant has already won first place and another contestant has won second place, there are 4 remaining contestants who are eligible for third place.
Step 4: Multiply the number of possibilities at each stage.
To find the total number of possibilities, multiply the number of possibilities at each stage: 6 × 5 × 4 = 120.
Therefore, there are 120 different ways that first, second, and third place can be awarded in this singing competition.