Category: Permutation and Combination

Question Number 21404 by Tinkutara last updated on 23/Sep/17 $$\mathrm{Prove}\mathrm{that}\left(6n\right)!\mathrm{is}\mathrm{divisible}\mathrm{by}{2}^{2n}.3^n.$$ Answered by dioph last updated on 23/Sep/17 $$\mathrm{if}n>1,\mathrm{there}\mathrm{are}\mathrm{at}\mathrm{least}3n\mathrm{even}$$$$\mathrm{numbers}\:\mathrm{and}\:\mathrm{2}{n}\:\mathrm{multiples}\:\mathrm{of}\:\mathrm{3}\:\mathrm{in} \…

Question Number 86684 by john santu last updated on 30/Mar/20 $$\mathrm{If}{(1+\mathrm{px}+{\mathrm{qx}}^2)}^8=1+8\mathrm{x}+{52\mathrm{x}}^2+{\mathrm{kx}}^3+\dots$$$$\mathrm{find}\mathrm{p},\mathrm{q}\mathrm{and}\mathrm{k}.$$ Answered by jagoll last updated on…

Question Number 151832 by DELETED last updated on 23/Aug/21 Answered by DELETED last updated on 23/Aug/21 $$57).{\mathrm{R}}_{\mathrm{s}}=2\mathrm{R}+2\mathrm{R}=4\mathrm{R}$$$$\frac{1}{{\mathrm{R}}_{\mathrm{p}}}=\frac{1}{2\mathrm{R}}+\frac{1}{4\mathrm{R}}=\frac{3}{4\mathrm{R}}$$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{R}_{\mathrm{p}} =\frac{\mathrm{4R}}{\mathrm{3}}\: \…

Question Number 151823 by DELETED last updated on 23/Aug/21 Answered by DELETED last updated on 23/Aug/21 $$\mathrm{54}.\:\:\mathrm{R}_{\mathrm{1}} :\mathrm{R}_{\mathrm{2}} =\rho\frac{\mathrm{l}_{\mathrm{1}} }{\pi\mathrm{R}_{\mathrm{1}} ^{\mathrm{2}} }:\rho\frac{\mathrm{l}_{\mathrm{2}} }{\pi\mathrm{R}_{\mathrm{2}} ^{\mathrm{2}} }…

Question Number 151485 by liberty last updated on 21/Aug/21 Answered by iloveisrael last updated on 21/Aug/21 $$N\left(A\right)=\frac{5!}{3!}\times \frac{7!}{2!}=\frac{120}{6}\times \frac{5040}{2}$$$$=20\times 2520=50400$$ Terms of Service Privacy…