In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 10 boys and 7 girls are competing, how many different ways could the six medals possibly be given out?
Question
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 10 boys and 7 girls are competing, how many different ways could the six medals possibly be given out?
Solution
To solve this problem, we need to calculate the number of ways the medals can be given out separately for boys and girls, and then multiply these two numbers together.
-
For the boys, there are 10 competitors and 3 medals to be given out. The number of ways to give out these medals is the number of permutations of 10 items taken 3 at a time. This is calculated as 10P3 = 10! / (10-3)! = 1098 = 720.
-
For the girls, there are 7 competitors and 3 medals to be given out. The number of ways to give out these medals is the number of permutations of 7 items taken 3 at a time. This is calculated as 7P3 = 7! / (7-3)! = 765 = 210.
-
To find the total number of ways the six medals can be given out, we multiply the number of ways for the boys and the girls. So, 720 * 210 = 151200.
Therefore, there are 151200 different ways the six medals could possibly be given out.
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 = 35C.Combination; number of ways = 210D.Permutation; number of ways = 210
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
Answer the questions below.(If necessary, consult a list of formulas.)(a) 63 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed?(b) A certain committee consists of 16 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.
62 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed?
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.