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At a competition with 7 runners, 2 medals are awarded for first and second place.

Each medal is different. How many ways are there to award the medals?

At a competition with 7 runners 2 medals are awarded for first and second place Each medal is different How many ways are there to award the medals class=

Respuesta :

Answer: C) 42

There are 7 ways for the first place winner to be chosen. Once that position is locked up, there are 6 ways to have someone picked for second place (since that first place runner can't simultaneously be in both places at once)

So we have 7*6 = 42 different permutations.

The longer way to get this answer is to use the permutation formula as shown below

nPr = (n!)/(n-r)!

7P2 = (7!)/(7-2)!

7P2 = (7*6*5!)/(5!)

7P2 = 7*6  <---- note how this shows up, as we found earlier

7P2 = 42

Either way, the answer is 42

Permutation is the arrangement of the objects or the things in a fixed order. There are total 42 number of ways to award the medals.

Given Information-

Total number of the competitors are seven.

Total numbers of the awards are 2.

The awards are given to the first and the second place competitors.

As all the competitors compete for the first place and one of them can be the the competitors who will finish at the first place. Thus the number of competitors who can get the first place medal is 7.

Now as the first place medal is won by a one runner hence only six competitors are left. The number of the competitors who can get the second place medal is 6.

This can be solve by the permutation methods.

What is permutation?

Permutation is the arrangement of the objects or the things in a fixed order. The number of the ways to award the medals are,

[tex]n_P_r=\dfrac{n!}{n-r!}[/tex]

[tex]7_P_2=\dfrac{7!}{(7-2)!}[/tex]

[tex]7_P_2=\dfrac{7!}{5!}[/tex]

[tex]7_P_2=\dfrac{7\times6\times5!}{5!}[/tex]

[tex]7_P_2=42[/tex]

Thus there are total 42 number of ways to award the medals.

Learn more about the permutation here;

https://brainly.com/question/1216161

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