Create two different situations: one in which you use combinations and one in which you use permutations. Include specific details and an explanation about what makes each situation either a combination or permutation.
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Permutation
A safe lock is a permutation lock, because the order does matter it is a permutation. In other words a permutation is an ordered combination.
Combination
There is no repition in lottery numbers (14,27,33,2,15,30). A combination is an order that does not matter without repition.
Permutation: If you are having a race with 10 people, there are 720 different ways that runners can finish the race. Since the order matters, this is a permutation.
10 x 9 x 8 =720
Combination: If you are selecting 3 members to join a club from a class of 10 students, there are 120 different clubs that can be formed. Since the order they are chosen doesn't matter, this is a combination.
(10 x 9 x 8) / 6 = 120
I know in late but good job
Fred goes to the adoption center and finds that they have 10 kids in total, Fred chooses to look at 5 of the ten kids, how many possible combinations are there?
bot please help
To solve this problem, you can use the combination formula:
nCr = n! / r! (n - r)!
where n is the total number of items (kids) and r is the number of items (kids) you want to select.
In this case, n = 10 and r = 5, so the formula becomes:
10C5 = 10! / 5! (10 - 5)! = 252
Therefore, there are 252 possible combinations of 5 kids that Fred can choose from the 10 kids in the adoption center.
Jack haves 10 more books to read but has 5 more how many permutation are there? help bot
I'm sorry, I'm not sure I understand the question completely. Are you asking how many permutations there are if Jack has 10 books to read and then has an additional 5 books to read for a total of 15 books? Or is there another scenario you are referring to? Please clarify so I can assist you better.
Create two different real-world scenarios—one in which you would use permutations and one in which you would use combinations:
Include specific details and an explanation about what makes each situation either a combination or permutation.
Provide sample data and calculate the total number of possible permutations and combinations for both scenarios.
Scenario 1: Permutations
You are organizing a running race with 10 participants. You want to know how many different ways the top 3 winners can finish the race. Since the order matters when identifying the winners, we use permutations to calculate the total possible outcomes.
To determine the number of possible permutations, we use the formula:
nPr = n! / (n - r)!
where n is the total number of participants and r is the number of winners we are interested in.
In this case, n = 10 and r = 3, so the formula becomes:
10P3 = 10! / (10 - 3)! = 720
Therefore, there are 720 possible permutations of the top 3 winners for a 10-participant race.
Scenario 2: Combinations
You are selecting 8 people out of a group of 20 to go on a trip. Since the order in which the 8 people are selected does not matter, we use combinations to calculate the total possible outcomes.
To determine the number of possible combinations, we use the formula:
nCr = n! / r!(n - r)!
where n is the total number of people and r is the number of people we are interested in selecting.
In this case, n = 20 and r = 8, so the formula becomes:
20C8 = 20! / (8! x (20 - 8)!) = 125,970
Therefore, there are 125,970 possible combinations of 8 people that can be selected from a group of 20 for the trip.