At a competition with 6 runners, medals are awarded for first, second, and third places. Each of the 3 medals is different. How many ways are there to award the medals?Decide if this is a permutation or a combination, and find the number of ways to award the medals.A.Combination; number of ways = 120B.Combination; number of ways = 20C.Permutation; number of ways = 20D.Permutation; number of ways = 120
Question
At a competition with 6 runners, medals are awarded for first, second, and third places. Each of the 3 medals is different. How many ways are there to award the medals?Decide if this is a permutation or a combination, and find the number of ways to award the medals.A.Combination; number of ways = 120B.Combination; number of ways = 20C.Permutation; number of ways = 20D.Permutation; number of ways = 120
Solution
This is a permutation problem because the order in which the medals are awarded matters (gold, silver, and bronze are not the same).
In a permutation problem, we use the formula nPr = n! / (n - r)!, where n is the total number of options, r is the number of options chosen at a time, and "!" denotes a factorial, which means multiplying all positive integers up to that number.
Here, we have 6 runners (n = 6) and we are awarding 3 medals (r = 3).
So, the number of ways to award the medals is 6P3 = 6! / (6 - 3)! = 654 = 120.
So, the answer is D. Permutation; number of ways = 120.
Similar Questions
At a competition with 7 runners, medals are awarded for first, second, and third places. Each of the 3 medals is different. How many ways are there to award the medals?Decide if this is a permutation or a combination, and find the number of ways to award the medals.A.Permutation; number of ways = 35B.Combination; number of ways = 210C.Combination; number of ways = 35D.Permutation; number of ways = 210SUBMITarrow_backPREVIOUS
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.A.Permutation; number of ways = 120B.Combination; number of ways = 120C.Permutation; number of ways = 1D.Combination; number of ways = 1
At a competition with 6 runners, 2 medals are awarded for first and second place.Each medal is different. How many ways are there to award the medals?A.720B.15C.30D.36
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 6 boys and 14 girls are competing, how many different ways could the six medals possibly be given out?
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?A.21B.5040C.49D.42SUBMITarrow_backPREVIOUS
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.