Number of 4-Digit Codes With and Without Repetition | Combinatorics, Permutations

How many 4 digit codes can be made using the digits 0 through 9? It depends on whether or not we allow repetition, or if we enforce any other weird rules. In today's video combinatorics lesson we'll figure out how many 4 digit codes we can make with and without repetition!

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SOLUTION TO PRACTICE PROBLEM:

There are 5 even numbers we can choose from when making our 4 digit codes (0, 2, 4, 6, and 8). We are not allowing repetition, so there are 5 numbers that can go first, 4 that can go second, 3 that can go third, and 2 that can go last. Thus, there are 5*4*3*2 = 120 4-digit codes using the even digits and not allowing repetition.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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[liamcgee]

Wow thanks, you made this so easy to understand. Was wrapping my head around trying to figure out how many possible 7 digit codes could I generate from a pool of 27 digits using repetition.

[espiritujoelyneb.]

Thank you for making it easy to understand

[happymeal]

Thank you so much for showing both examples of repeat digits and no repeats. :)

[zorx]

3:49 can you explain how can there be 10 possibilities of putting first digit, because if we put 0 as first digit, it will make whole a 3 digit no. (Eg. 0329. Zero neglected, which make it a 3 digit rather than 4)
So I think there should be 9 ways of putting first digit rather than 10

[minjugatto]

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First of all I wanna thank YOUTUBE....

[danishsayyed]

Sir, we are asked to make a four digit number using 0 to 9 i.e 10 options . So, if we make these with or without repetition the number 0 if used as a thousands digit number would not make a four digit number. So, sir I think there are 9 possible options form the thousands place.

[zaraivana]

I have been having a hard time understanding this topic 'til I watched this video. Thank you Sir. You just earned a follower. Hoping you could make a video about the same topic but with different restriction like only divisible by a number.

[memecage]

Thank god you exist. Super duper helpful

[georgenicholas]

Is there a formula I can use in Excel to provide me a list of individual 4-digit combinations without repetition? I've forgotten the combination to a Masterlock key box that uses pushbuttons that can only be used once. Thanks in advance!

[karandudeja]

Interesting effects going on there 😊

At around 5:11 in the video, you mentioned the formula P(10, 4)... Now is it possible to have a situation in Permutations where the formula becomes P(4, 10) ?

I'm sorry if this comes across as a stupid question. I'm trying to figure out Permutations for a project. Thanks in advance.

[Winedineandrhyme]

but what if i'm trying to find the probability that number has at least one digit repeated?

[MurrayLouw]

From your homework problem "Thus, there are 5*4*3*2 = 120 4-digit codes using the even digits and not allowing repetition.", can you show this in your P(x, y) format as well?

[deidrecoltrane]

I have a request.... could you take a look at this to advise how this would be worked? I am a little confused.

You have been asked to create license plates for the City of Asheville, NC. Suppose license?
plates are to have three letters followed by three digits, and the first digit cannot be zero.

-How many different license plates can be made (replacement is okay)?

-How many different license plates can be made if letters cannot be duplicated?


Thank you in advance

[landysenne]

Good day please assist on this how many code words over a, b, c, d of length 20 contains exactly 10 a's?

[muslimumer]

thank you for makin it easy to undersanding

[StophD]

What about a four digit code with 0-9, but working out how many of the same number? e.g. four matching digits there's 10 possible codes, so how many have three matching numbers in any position? Or two digits etc

[louiesaunders]

Can anyone help me with a harder question - For the first two digits use an odd number between 39 and 100, for the last two digits use a multiple of 10, repetition is allowed work out the total number of codes which can be made using the method

[indomitablesin]

Sir, at 7:01 you have taken total of 6 possibilities for the thousandth's place, however those possibilities also include 0, which would effectively make the proposed 4-digit number in a 3-digit number.

What do we do?

[cyrusemotin]

I get it i do my module but i don't understand how thanks for your example 💖💖💖

[The_uniquerat]

How do you write something like this into an expression? I understand where the 10 ^P 4 comes from and know how to calculate that with the function and stat feature on my calculator, but I am needing to learn how to write equations such as this into an equation and cannot grasp the concept. Hopeful. Jenn