Question

At a competition with 5 runners, 5 medals are awarded for first place through

fifth place. Each medal is different. How many ways are there to award the
medals?
Decide if the situation involves a permutation or a combination, and then find
the number of ways to award the medals.
​

Answer 1

Answer with explanation:

Number of runner= 5

Number of Distinct Medal = 5

First Medal can be Awarded in 5 ways, second Medal can be awarded in 4 ways and third Medal can be awarded in 3 ways , fourth medal can be awarded in 2 ways and fifth Medal can be awarded in one way.

So, total number of ways =5 × 4×3×2×1=120 way

⇒We will use the concept of Permutation as there are five distinct medal and five different runners

So, Five distinct places can be filled in 5! or
`_(5)^(5)\textrm{P}` ways as order of arrangement is Important because any of the five candidates can win first second, third , fourth or fifth Prize.

= 5!=5×4×3×2×1=120 ways

Because, n!=n×(n-1)×(n-2)×........1.

Answer 2

Answer: Permutation; number of ways = 120

Explanation: