Unanswered Combinatorics Questions

\hspace{-16}\bf{(1)\;\;}$ Total Integer ordered pair,s of $\bf{(x,y)}$ in $\bf{x^2-y! = 2001}$\\\\\\ $\bf{(2)\;\;}$ Total Integer ordered pair,s of $\bf{(x,y)}$ in $\bf{x^2-7y! = 2011}$\\\\\\ $\bf{(3)\;\;}$ Total Integer orde ...

There are 5 different red balls,5 different green balls,5 different blue balls and 5 different black balls.In how many ways can they be arranged so that no two balls of same color are adjacent ? ...

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If m men and n women are to be seated in a row such that no two women seat together,then find the ways in this can be done. ...

number of permutations of taken all at a time such that the digit 1,2,3,4,5,6,7,8,9 appearing somewhere to the left of 2. 3 appearing to the left of 4. 5 appearing to the left of 6. eg 815723946 ...