Question

Please help at a competition with 5 runners, medals are awards for first second and third place each of the 3 medals is diffrent how many ways are there to award the medals?

decide if this is a permutation or a combination and find the number of ways to award the medals

Answer 1

60 ways

Explanation:

Solution:-

- There are 5 runner competing in a race. There are 3 awards available. Any of the three runners will be awarded ( Gold, Silver and Bronze) medals.

- We see that there can be only 3 designated awardees of the medals. One runner can only get 1 medal. And the possibility of ties are ruled out.

- We are to "select" (Combination) the number of people who could possibly each award.

For Gold = 5 possible runner but only 1 gets them , 5C1 = 5

For Silver = 4 possible runner but only 1 gets them, 4C1 = 4

For Bronze = 3 possible runner but only 1 gets them, 3C1 = 3

- The total number of ways to award the medals would be:

Total ways = Gold*Silver*Bronze

= 5*4*3

= 60 ways

Answer 2

Permutation; 60 ways

Explanation:

In this question, we are asked to determine if what to use is a permutation or a combination and proceed to determine the number of ways to award the medals.

now, to determine if what to use at a particular scenario is combination or permutations, we need to know the whether we are selecting or we are arranging. when we are selecting, this is a combination issue while we are arranging it is a permutation issue.

as seen from the question, it is a matter of position, thus indicating that we are making an arrangement, meaning we are to use permutation.

Now, we calculate the number of ways;

we are awarding 3 medals to a total of 5 people.

the number of permutations here is simply;

5P3 =5!/(5-3)! = 5!/2! = 60 ways