7 participants participated in the competition，and there 3 of them will won a price and be ranked as 1st, 2nd and 3rd. How many possible combinations are there for the top 3 spots
Question
7 participants participated in the competition，and there 3 of them will won a price and be ranked as 1st, 2nd and 3rd. How many possible combinations are there for the top 3 spots
Solution
This is a permutation problem because the order in which the participants are ranked matters.
The formula for permutations is:
P(n, r) = n! / (n-r)!
where:
- n is the total number of options,
- r is the number of options chosen at a time,
- "!" denotes a factorial, which means multiplying all positive integers up to that number.
In this case, n = 7 (the total number of participants) and r = 3 (the number of spots to fill).
So, the calculation would be:
P(7, 3) = 7! / (7-3)!
= 7654321 / 432*1
= 765
= 210
So, there are 210 possible combinations for the top 3 spots.
Similar Questions
From a group of 9 people, select the best 3 players to represent the group to participate in the team competition. How many total possibilities are there?
Seven cash prizes of distinct amounts are to be awarded to 3 runners who finish in the first, second and third positions, such that each runner gets at least one prize. In how many ways can it be done if the smallest cash prize received by any runner is greater than the highest cash prize received by any runner who finished after him?
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?
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
A gymnastics competition has 4 gymnasts. How many different top-3 rankings are possible?
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.