Question

2 Points

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.
O
A. Combination; number of ways = 1
O
B. Combination; number of ways = 120
O
C. Permutation; number of ways = 1
O
D. Permutation; number of ways = 120
SUBMIT
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Answer 1

Option: D is the correct answer.

D. Permutation; number of ways = 120

Explanation:

We need to use the method of permutation since permutation method is used for the selection as well as arrangement of the 5 students.

Now there are 5 competitors in a running competition and 5 medals are awarded for first place through fifth place. Each medal is different.

Now, the ways it can be done is:

`5_P_5=(5!)/((5-5)!)\\\\\\5_P_5=(5!)/(0!)\\\\\\5_P_5=5!\\\\\\5_P_5=5* 4* 3* 2* 1\\\\\\5_P_5=120`

Hence, option: D is the answer.