General Discussion

General DiscussionTotal combinations of draft possible

Total combinations of draft possible in General Discussion
AnŦaiN

    If someone has good Maths here , i would like to ask him the following question which came to my mind but couldn't solve .
    There are 115 heroes , 5 in our team , 5 in enemy team . If we play some amount of games , such that in every game , at least one hero is different in our team OR one hero is different in their team , how many total drafts are possible ?
    Also explain which method u used as i couldnt solve .

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    Sixe史吏

      115 heroes. 5 heroes to Radiant, 5 different heroes to Dire.

      There is 115 Choose 5 = 115! / (5! * 110!) ways to choose Radiant's heroes.
      Given that Radiant has already chosen, there is now 110 remaining heroes. There is 110 Choose 5 = 110! / (5! * 105!) ways to choose Dire's heroes.
      Thus, the answer is to multiply the number of ways to choose Radiant's heroes with the number of ways to choose Dire's heroes. That is: 115 * 114 * 113 *... *106 / (120)^2 = 18784179344417256

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      Prodigy

        Dont stress ur mind with this thing

        Kotato

          do stress your mind, combinatorics is a great excersice for the brain!

          vygin

            Quick mafs solves everything just do it !

            AnŦaiN

              Just had this idea while permutation topic was going in class , but havent completely studied it so i understood first part and not the second one , but dont worry i will later . Sixe ty

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              Feachairu

                wait wat the hell does that sixe guy mean,my brain hurts
                explain pls

                AnŦaiN

                  ^^Its a thing relating to factorials and permutation , I wouldnt bother researching it if not good at maths or no interest in maths . Just know that u can play 18784179344417256 matches without repetition in the draft of the overall game . It is a mindblowing amount , and another proof that dota is something that even if u play hundreds of thousands of hour ,u cant just get so good at it ,that u dont have to think anymore .

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                  Feachairu

                    wat the hell
                    but what if you shorten it into a meta hero only

                    AnŦaiN

                      How many are meta heroes ?

                      Autumnus

                        I love math

                        A̶𝖘𝖍𝖊𝖘

                          Reminds me of the permutations and combination classes at school n college. Good old times , one of the most interesting topics in math which you can apply in all industries.

                          AnŦaiN

                            ^^^
                            Dude u sound like a 50 year old

                            Dukeus

                              i dont think its right.

                              Had the same idea as sixe but there will be a lot of match ups that appear double.
                              You can not just multiply (115 5)*(110 5)

                              Example:
                              5 heros in total and you can pick 2 per team
                              Answer would be 30 with math above
                              its actually only 15
                              you can write it down

                              Or am I retarded its late

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                              Saya Tidak Takut, Hadapi ...

                                dukeus is right

                                AnŦaiN

                                  ^^^^
                                  U guys just dont know permutation and combination . I cannot tell u the reasons , it will be like teaching algebra to someone who barely knows counting .

                                  Dukeus

                                    Lol what. I just pointed out a mistake. I am right.

                                    I give you the correct answer when i have time on the weekend and find my old math book

                                    Alpha

                                      Simple combination: 115Choose5 x 110Choose5
                                      Same as what Sixe elaborated.

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                                      AnŦaiN

                                        U are rusty in maths dukeus xDDDDD

                                        Alpha

                                          DotA players talking maths makes me to hate it a lot lesser

                                          LucaManny

                                            @dukeus : Its 30 because you count radiant and dire different

                                            If you take radiant and dire as the same e.g: AB vs CD is the same as CD vs AB then u need divide the formula by 2!

                                            Totentanz to The King: M ...

                                              i dont wanna be some r/iamverysmart material here but do you guys actually struggle with this entry level combination problem and fail to understand it?

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                                              Cratyz

                                                2+2 = 4

                                                Alpha

                                                  @duchass: 115C5 x 110C5 is same as 110C5 x 115C5.
                                                  We r doing 10 selections only. Counting one as team 1 and the other team 2 with 5 players each.
                                                  There's no need to divide again

                                                  Alpha

                                                    2x2=4
                                                    ..
                                                    Dividing by 2+2=4
                                                    We get
                                                    x/+ =1
                                                    Hence x=+

                                                    Dukeus

                                                      @LucaManny

                                                      Yeah thats what i meant.
                                                      I thought ab vs cd is the same as cd vs ab. Its the same match up. Thats what i try to say.

                                                      So you have to divide the result by 2 to get the answer op wanted in my opinion.

                                                      Sry should take my time and explain things better next time i write something. Thx for help

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                                                      AnŦaiN

                                                        @perdita , u are trying to be r/iamverysmart cuz i just told i havent studied the whole topic .