Question

gold ,silver,bronze medal are awarded in an olympic event.in how many posible ways can the medals be awarded for a 200 meter sprint in which there 12 runners

Answer 1

Step-by-step explanation:

A gold, a silver and a bronze are awarded in an Olympic Event. So, getting gold medal is not same as getting silver medal. So, this is a permutation problem as order matters.

Possible ways=P(n,k)

P(n,k)=n/(n-k)

n= 9 members

k= 3 medals

P(n,k)= 9/(9-3)

= 9/6

=9•8•7•6/6

= 9•8•7

=504

Answer 2

Answer:

There are 1320 ways in which 12 runners can be awarded for a 200-meter sprint race three different medals.

Step-by-step explanation:

• Whenever we are supposed to find the ways in which certain things have to be arranged, we use the concept of Permutation.
• Permutation determines the number of possible ways an element can be arranged.
• Here the order of the arrangement matters.

SOLVING:

In an olympic event getting a gold medal is not equal to getting a silver or a bronze medal. Hence, we will use the concept of permutation for this problem as order matters here.

Possible ways = $p (n,k)$

where n = number of runners

and k = number of medals

= $n!/ (n-k)!$

$= 12! / ( 12 - 3 )!$

$= 12 !/ 9!$

= $12*11*10$

= $1320$

Hence, there are 1320 ways in which 12 runners can get these 3 medals.