Question

a group of 20 people are going to run a race the top three runners on gold silver and bronze medals how many different ways are there to award the medals?​

Answer 1

Answer:

A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals. = 32,760 " 4SPE = 85,140 15'4

Step-by-step explanation:

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Answer 2

Concept:

To solve this problem, let's recall the concept of permutation.

A permutation is the arrangement of things that can be done taking some or all of it at a time.

Formula to be used: ⁿPₓ=$\frac{n!}{(n-r)! r!}$

Given:

20 people running a race

To find:

Different ways to award the medals

Solution:

We are to arrange three award winners out of 20 participants such that one wins one of the medals (say gold), one wins another(say silver) and one wins the last left(say bronze medal).

Now, the gold medal can be awarded to one person from the 20 people.

After, giving away the gold medal to one, there are 19 left, silver can be awarded to one person from the 19 people.

Lastly, after giving away 2 medals 18 people are left. So, one person can be awarded a silver medal out of 18 people.

Hence, the total no of ways to award the medals is

=²⁰P₁x¹⁹P₁x¹⁸P₁    (using the formula ⁿPₓ)

=$\frac{20!}{(20-1)!1!}X$$\frac{19!}{(19-1)! 1!} X$$\frac{18!}{(18-1)! 1!}$  

=20x19x18

=6840

Hence, the number of ways the medals can be awarded is 6840 ways.