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Category: Permutation and Combination

How-many-rearrangements-are-there-of-the-letters-in-the-world-i-ENGINEERING-ii-MATHEMATICAL-

Question Number 133314 by bramlexs22 last updated on 21/Feb/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{rearrangements}\:\mathrm{are}\: \\ $$$$\mathrm{there}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{in}\:\mathrm{the}\:\mathrm{world} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{ENGINEERING} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{MATHEMATICAL}\: \\ $$ Answered by EDWIN88 last updated on 21/Feb/21…

It-is-required-to-seat-5-men-and-4-women-in-a-row-so-that-the-women-occupy-the-even-place-How-many-such-arrangements-are-possible-

Question Number 132854 by EDWIN88 last updated on 17/Feb/21 $$\mathrm{It}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to}\:\mathrm{seat}\:\mathrm{5}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\: \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{women}\:\mathrm{occupy}\:\mathrm{the}\:\mathrm{even}\: \\ $$$$\mathrm{place}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{such}\:\mathrm{arrangements}\:\mathrm{are} \\ $$$$\mathrm{possible}\:?\: \\ $$ Answered by bramlexs22 last updated on 17/Feb/21…

it-is-a-known-that-a-particular-machine-will-make-product-with-a-qualified-rate-of-90-when-it-is-running-well-but-will-do-so-with-a-qualified-rate-of-only-30-when-it-is-not-running-well-The-

Question Number 132439 by liberty last updated on 14/Feb/21 $$ \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{known}\:\mathrm{that}\:\mathrm{a}\:\mathrm{particular} \\ $$$$\mathrm{machine}\:\mathrm{will}\:\mathrm{make}\:\mathrm{product}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{90\%}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{running}\:\mathrm{well},\:\:\mathrm{but}\:\mathrm{will}\:\mathrm{do}\:\mathrm{so}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\:\mathrm{rate}\:\mathrm{of}\:\mathrm{only}\:\mathrm{30\%}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{not}\:\mathrm{running}\:\mathrm{well}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{machine}\:\mathrm{is}\: \\…

What-is-the-coefficient-x-10-in-the-expansion-of-1-x-2-x-3-8-

Question Number 132382 by liberty last updated on 13/Feb/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{x}^{\mathrm{10}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} −\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{8}} \\ $$ Answered by EDWIN88 last updated on 13/Feb/21 $$\mathrm{by}\:\mathrm{multinomial}\:\mathrm{theorem}\:;\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{10}} \\…