Permutations with Repetition | Combinatorics, Permutations and Combinations

How do we count permutations when repetition is allowed? Problems like counting how many 4-digit codes can be created with the digits 0-9 - allowing repetition of digits - cannot be solved using the permutation formula. As it turns out, the permutation formula is more complicated than anything we need to solve the sort of problems we’re talking about today. We’ll be talking about permutations with repetition in today’s combinatorics video lesson!

For example, how many 4-digit codes can be created using the digits 0-9 without repetition? There are 10 choices for the first digit, but repetition is not allowed, so there are only 9 options for the second digit, 8 for the third, and 7 for the fourth. Thus, there is a total of 10*9*8*7 possible 4-digit codes in this situation.

What if repetition is allowed? Then there are 10 options for all 4 digits! Thus there are 10*10*10*10 = 10^4 total options. So if we have a collection of n objects, and are ordering r of them, and repetition is allowed, then there is a total of n^r permutations possible! Check out the full video lesson for more details and examples!

SOLUTION TO PRACTICE PROBLEM:

In this problem, the collection size is 26, there are 26 letters to choose from. We are ordering 7 of them because we are counting the number of 7 letter passwords. Repetition of letters is allowed. There is a total of 26^7 permutations of 7 letters from a collection of 26 when repetition is allowed. Simple as that, 26^7 is the answer!

If repetition was not allowed, the answer could be found using the permutation formula P(26, 7) = 26*25*24*23*22*21*20 = 26!/19!.

I uploaded this video a couple of days ago, but didn't like how I explained one thing, so I fixed it, and took down the old one!

********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.

********************************************************************

+WRATH OF MATH+

Follow Wrath of Math on...

[Yang_TK]

This saved me, thank you very much 🙏🙏🙏

[cellsubs]

Thank you for this video!
I have a question about the permutation with repetition.
Here is the question: There are 3 pigeon holes marked A, B, C. In how many ways can I arrange 10 different postcards so that 5 of them are in A, 3 in B and 2 in C?
For this question, should I divide 10! by (5! 3! 2!)?

[stanleytaylor]

If 26 letters are used for a 7-word password and repetitions are allowed, then the number of passwords is 26^7 (26 multiplied by itself 7 times). This is about 8 billion possible passwords. If both capitals and lowercase letters are allowed, the answer is 52^7, or about 1 trillion. I would go for both uppercase and lowercase letters when creating such a password.

[martyjehovah]

I was curious about how many sets of 3 colors were possible from a pool of 16 colors, so i went to google to find out how to calculate it, and then i spent 5 minutes learning about the difference between "combination" and "permutation". Then, after another 10 minutes, I was even more confused than when I started out, because I couldn't make the formula make sense. Then by sheer luck I realized the formula was so complex (to me) because it wasn't allowing for repetition and so it wasn't even the answer I was looking for, but when I saw the formula for permutation with repetion it didn't really make logical sense to me either.

I was about to give up on being able to actually learn how to answer this sort of question on my own, when I found your video! Your break down of what the formula was actually doing and your summary that "the total number of possibilities is the collection size to the power of the number of objects we're ordering" was perfectly plainly stated. You turned something confusing that I'd only be able to use by memorization or looking it up every time, into something that is just an obvious logical process that I will remember both how to use it, and WHY it works forever. Thank you!

I can't wait to find out what else I can learn from you.

[alanfinck]

so what exactly is the "assassin" example called? permutation with already existing repetition?

[deepaksarvepalli]

Today feeling so happy becoz of ur Video, why because permutations with repetition is what u said is awesome but others make people confuse by saying the example u

[ShukronaUmerova]

I didn't understand this topic, I learned it after your video and it was very helpful! Thank you very much! Good luck!

[KaidenPvP]

6:20 Here is the answer




There are 8, 031, 810, 176 ways to make a 7 letter password with permutation with repetition (26^7)

[Ghost_Cube]

Giga Chad YouTuber, finding the best way to write ass twice

[malikibetche]

May God bless you, you helped me a lot !!!

[AubreeGames]

Thank you. Very helpful and nice video

[shekharchauhan]

@Wrath of Maths can you please create separate playlist for discrete mathematics

[deepaksarvepalli]

U r awesome with min subscibers.... Wish you all the best

[trickdigger]

Thanks for the nice class. Great work sir.

[salton]

ez. multiply 26 seven times ☺☺😂😂😂😂☺☺☺☺🤑🤑😎😎😎😎😎😎