[Discrete Mathematics] Combinations with Repetition Examples

In this video we look at positive integer solutions, as well as a problem with pseudocode.

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[SarbbottamBandyopadhyay]

👏🏼👌🏼Fantastic! Never realized combination could be used to find out the number of iteration.

The loop in JavaScript if any one is curious
count = 0;
for (i = 1; i <= 20; i += 1) {
for (j = 1; j <= i; j += 1) {
for (k = 1; k <= j; k += 1) {
for (m = 1; m <= k; m += 1) {
count += 1;
}
}
}
}
console.log(count); // 8855

The result is the same as 23!/(4!.19!) = 8855

[ajayjadhav-vcwg]

Good series of lectures and examples, Thanks! BTW your voice is awesome!

[chaitrajambigi]

Hello, great explanation! I have a doubt in this last code snippet, when we are choosing 4 numbers from 20 with repetition, how are we ensuring that the condition m<=k.. is maintained?

[annulrsolformrkelse]

Thanks for this great video. I found everything very helpful.
I only have one question regarding the last exercise (pseudo-code): Why do we not have to account for different orders? I thought we had to account for them as well, since for example the solution i=1, j=2, k=3, m=4 is not the same as i=2, j=3, k=4, m=1, or am I wrong?
Thanks a lot to anyone who can help.

[icecoolguita]

On the last problem, can someone explain to me how 23 choose 4 accounts for selecting the elements in ascending order?

On a side note, thanks for doing this series

[code_with_aakash]

a=0
for i in range (1, 20+1):
for j in range(1, i+1):
for k in range(1, j+1):
for m in range(1, k+1):
a=a+1

I executed the following python code in my shell and at the end a was 8855 which is not equal to C(23, 4).Can you please tell me where I went wrong ?

[ahmedturner]

For the second question, why isn't 0 considered a positive integer before converting the x and y's to prime?

[eimaldorani]

Too confused! :(
@last example @07:30 isn't it (23 choose 20) = (23 choose 3) !?

[morhadi]

Why is simply not 20 raised to power 4?

[josipbalaban]

how would you do the following problem: you are responcible for distributing 34 candies to 8 children, however the amount of candy each child gets must be an even number (including 0). How many ways can you do this?

[andrewhe]

what will happen when i say " n - 19 = n - 64 " in question 2 ?

[syedmdabid]

At first try to know who discovered the repeated combination and when, then know all about this.