i am sorry. of course i know binomial theorem. we are learning that in 10th grade but i coudn't do anythingYou should know by now that you get help after you show work.
Do you know the binomial theorem?
In order to help, we need to see what you know, and where you are stuck.i am sorry. of course i know binomial theorem. we are learning that in 10th grade but i coudn't do anything
To Sayo, please tell us about the topics that you have studied in connection with this assignment.i am sorry. of course i know binomial theorem. we are learning that in 10th grade but i coudn't do anything
That is what I wrote!There are several ways to do this.
It is an example of 'stars and bars' (if you are familiar with this).
[MATH](1+x+ .... + x^{100})(1+x+ .... + x^{100})(1+x+ .... + x^{100})[/MATH]We want to pick a term from each bracket so that when we multiply the three terms together, the powers add up to 111.
We want to count all such combinations.
I.e. how many integer solutions are there to:
[MATH]x_1+x_2+x_3=111[/MATH]with [MATH]0≤x_i≤100[/MATH]
Assuming you are familiar with 'stars and bars', here is a similar (but more difficult) example.
View attachment 28062
Note: your example is much simpler, since there can be a maximum of one of the variables >100.
Sorry - I didn't intend to steal your idea just to add to it by making explicit that this is an example for 'stars and bars' and further, giving an example where there is a maximum to the value each variable can take.That is what I wrote!
(Also they add up to 111, not 101)!You need to count the number of ways that you can choose three numbers (repeats are allowed-why?)from the set 0, 1, 2, ..., 100 so the three numbers add up to 101.
Just having some fun at your expense.Sorry - I didn't intend to steal your idea just to add to it by making explicit that this is an example for 'stars and bars' and further, giving an example where there is a maximum to the value each variable can take.
If attempted this way, this example requires 'stars and bars' and PIE.
(Also they add up to 111, not 101)!
Not at all!Good! I didn't tread on your beard then!