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Question Number 104497 by PengagumRahasiamu last updated on 21/Jul/20

Commented by mr W last updated on 22/Jul/20

$$Q2:$$$$a⩽2?$$

Commented by PengagumRahasiamu last updated on 22/Jul/20

Non-negative integer Sir

Answered by mr W last updated on 22/Jul/20

$$supposea,b,...\in \mathbb{N}$$$$Q1:$$$${(x+x^2+x^3+x^4+x^5+x^6)}^4$$$$=x^4{(1+x+x^2+x^3+x^4+x^5)}^4$$$$=\frac{x^4{(1-x^6)}^4}{{(1-x)}^4}$$$$=x^4(1-4x^6+6x^{12}-4x^{18}+x^{24})\underset{k=0}{\sum ^{\mathrm{\infty }}}{C}_3^{k+3}{x}^k$$$$coefficientof{x}^{20}term:$$$$C_3^{19}-4\times C_3^{13}+6\times C_3^7=35$$$$\Rightarrow 35tuples$$$$$$$$Q2:$$$$0tuplesifa⩽2$$$$since2+3+4+5+6+7=27<30$$$$2520tuplesifa⩾1$$

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