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.
Question
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.
Solution
(a) The number of ways the 3 medals can be distributed is given by the permutation formula P(n, r) = n! / (n-r)!, where n is the total number of items, and r is the number of items to choose. Here, n = 63 (the total number of athletes), and r = 3 (the number of medals to be distributed). So, the number of ways the medals can be distributed is P(63, 3) = 63! / (63-3)! = 636261 = 238,266 ways.
(b) Similarly, the number of ways the 3 offices can be filled is given by the permutation formula P(n, r) = n! / (n-r)!, where n is the total number of items, and r is the number of items to choose. Here, n = 16 (the total number of committee members), and r = 3 (the number of offices to be filled). So, the number of ways the offices can be filled is P(16, 3) = 16! / (16-3)! = 161514 = 3,360 ways.
Similar Questions
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?
(a) 56 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) An experiment involves 31 participants. From these, a group of 4 participants is to be tested under a special condition. How many groups of 4 participants are possible?
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, 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
(b) A certain committee consists of 17 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.,840
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.