Question

In: Statistics and Probability

What is the difference between combinations and permutations?

What is the difference between combinations and permutations? Give details

Expert Solution

Let's say you choose a committee of three to represent your class of 30 students:

For the first member you have

30 choices

For the second you have

29

For the third you have

28

For a total of 30⋅29⋅28=24360 possible permutations

Now this is assuming that the order of choice is relevant: the first one will be called 'president', the second will be 'secretary' and the third will be just 'member'.

If this is not the case (all three are equal) then the order in which they are picked is not important.

With three picked there are 3⋅2⋅1

=3!=6

possible orders, which all give the same group. These are called combinations .

So: combinations= permutations divided by orders

Or, in our example:

24360/6=4060

It depends of whether the order is important.

Sankar Maity answered 2 years ago

What is the actual difference between linear combinations and Span , could you perhaps give me...

What is the actual difference between linear combinations and Span , could you perhaps give me a definition that can help me easily see the difference , maybe provide a visual aid too. Explanations of any other 'tricky' definitions in linear algebra would be of great help too and highly appreciated! Thank you in advance.

Part 1: Combinations and Permutations: Winning the Lottery To win the Powerball jackpot you need to...

Part 1: Combinations and Permutations: Winning the Lottery To win the Powerball jackpot you need to choose the correct five numbers from the integers 1 - 69 as well as pick the correct Powerball which is one number picked from the integers 1 - 26. The order in which you pick the numbers is not relevant. You just need to pick the correct five numbers in any order and the correct Powerball. Because there is only one correct set of...

Permutations and combinations. a.)A typesetter has before him 26 trays, one for each letter of the...

Permutations and combinations. a.)A typesetter has before him 26 trays, one for each letter of the alphabet. Each tray contains 10 copies of the same letter. In how many ways can he form a three letter word that requires at most two different letter? b.)Determine the number of ways of forming words which use exactly two different letters.

Pick any type of public lottery and find the probability of winning using combinations or permutations....

Pick any type of public lottery and find the probability of winning using combinations or permutations. Be sure to explain the rules to the lottery( how many numbers chosen, from what set of numbers, power ball numbers etc...) Then also explain how you achieved the probability you did. The lotteries could be from a different state or country as long as it is public

This week you learned about the addition and multiplication counting principles, permutations and combinations. Identify a real...

This week you learned about the addition and multiplication counting principles, permutations and combinations. Identify a real life example of where one of these principles can be used.

Use the Basic Counting Law, Permutations, or Combinations to answer the following: 1.) eleven drugs have...

Use the Basic Counting Law, Permutations, or Combinations to answer the following: 1.) eleven drugs have been found to be effective in the treatment of a disease. it is believed that the sequence in which the drugs are administered is important in the effectiveness of the treatment. In how many ways can 5 of the 11 drugs be administered?

1. Answer the following questions regarding permutations and combinations. How many different 5-digit octal numbers are...

1. Answer the following questions regarding permutations and combinations. How many different 5-digit octal numbers are there which do not contain the digit 0? How many different 5-digit octal numbers are there which do not contain the digit 0 and in which all digits are different? How many 5-digit octal numbers are there which do not contain the digit 0 and where the third digit is an odd number and the last digit and even number? How many different combinations...

What is the difference between a Eulerian Path and Circuit? What is the difference between a...

What is the difference between a Eulerian Path and Circuit? What is the difference between a Hamiltonian Path and Circuit? Is the image below Eulerian or Hamiltonian, Path or Circuit? How did you determine your answer?

What is the difference between a refrigerator and a heat pump? What is the difference between...

What is the difference between a refrigerator and a heat pump? What is the difference between a refrigerator and an air conditioner? Define the coefficient of performance of a refrigerator in words. Can it be greater than unity? Check the specification of refrigerator or air-conditioner at your home. See if you can obtain COP of the machine. A heat pump that is used to heat a house has a COP of 2.5. That is, the heat pump delivers 2.5 kWh...

what is the difference between:

what is the difference between:1. the ingression of cells in the chick versus the involution of cells in the frog.2. the movement of Hansen's node in the chick versus the lack of movement in the blastopore.