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2n-objects-of-each-of-three-kinds-are-given-to-two-persons-so-that-each-person-gets-3n-objects-Prove-that-this-can-be-done-in-3n-2-3n-1-ways-




Question Number 22036 by Tinkutara last updated on 14/Oct/17
2n objects of each of three kinds are  given to two persons, so that each  person gets 3n objects. Prove that  this can be done in 3n^2  + 3n + 1 ways.
$$\mathrm{2}{n}\:\mathrm{objects}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{three}\:\mathrm{kinds}\:\mathrm{are} \\ $$$$\mathrm{given}\:\mathrm{to}\:\mathrm{two}\:\mathrm{persons},\:\mathrm{so}\:\mathrm{that}\:\mathrm{each} \\ $$$$\mathrm{person}\:\mathrm{gets}\:\mathrm{3}{n}\:\mathrm{objects}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{done}\:\mathrm{in}\:\mathrm{3}{n}^{\mathrm{2}} \:+\:\mathrm{3}{n}\:+\:\mathrm{1}\:\mathrm{ways}. \\ $$
Commented by Tinkutara last updated on 14/Oct/17
help pls
$$\mathrm{help}\:\mathrm{pls} \\ $$

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