Aman Deep Gautam
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 Nov 11 awarded Notable Question Sep 6 awarded Popular Question May 29 awarded Popular Question May 21 comment Finding solutions to the equation @BabyDragon Thanks. Can we formulate this mathematically, like some generalization? May 21 revised Finding solutions to the equation added 146 characters in body May 21 asked Finding solutions to the equation Apr 3 comment Calculating number of connected graphs @DouglasS.Stones I think what I edited for clarification is creating doubts. Please see the edit. I think it should be clear now what I want to do. Apr 3 revised Calculating number of connected graphs added 114 characters in body; edited tags Apr 3 comment Calculating number of connected graphs @Hegen As I said "no other constraints like loop" i.e. graphs with loops are to be included. Apr 3 asked Calculating number of connected graphs Feb 8 accepted number of solutions for the equation Feb 4 accepted Number of ways of winning a particular kind of game Feb 4 comment Number of ways of winning a particular kind of game Got it. Confused your answer with my previous thoughts. That's why messed it up. It was easy question, should have got it at first go. Feb 4 comment Number of ways of winning a particular kind of game Please explain the reason why you don't think so. I might get convinced..:) Feb 4 comment Number of ways of winning a particular kind of game I wanted to count the number of ways $A$ win. And I think that it should be equal to the number of distinct permutations only. Am I thinking correctly? Feb 4 comment Number of ways of winning a particular kind of game I still do not understand. Please bear with me. Here is what I do not understand. Let us have two denominations $1$ and $2$. Now let there be 5 cards, namely, $1, 1', 1'', 2, 2'$ ($'$ are included just to differentiate cards of same denomination for discussion purposes). If choose a combination $1, 1', 2, 2'$ and $1', 1'', 2, 2'$ for A then this is only a way of winning(counted 2 times, if I use normal C(n, k) formula without any constraints.) as A has 2 cards of denomination 1 and 2 cards of denomination 2. Feb 4 comment Number of ways of winning a particular kind of game That I figured out on my own. What's next. I mean that since the cards of same denomination are identical I can't use direct C(n,k) formula. Feb 4 awarded Commentator Feb 4 comment Number of ways of winning a particular kind of game @BrianM.Scott Yes, essentially this is what it boils down to Feb 4 comment Number of ways of winning a particular kind of game @BrianM.Scott If there are $n_i$ $i^{th}$ numbered cards. Then A can get any number of cards from $n_i$ and the rest of the cards go with B. Same is repeated for all cards of all denomination. Then the score is calculated.