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Question Number 5989 by sanusihammed last updated on 08/Jun/16

Evaluate 10 ×12 × 14 × 16 × 18 × 20 into factorial form

$${Evaluate}\:\:\:\mathrm{10}\:×\mathrm{12}\:×\:\mathrm{14}\:×\:\mathrm{16}\:×\:\mathrm{18}\:×\:\mathrm{20}\:\:{into}\:{factorial}\:{form} \\ $$

Answered by prakash jain last updated on 08/Jun/16

10×12×14×16×18×20 =2(5×6×7×8×9×10)=((2!10!)/(4!))

$$\mathrm{10}×\mathrm{12}×\mathrm{14}×\mathrm{16}×\mathrm{18}×\mathrm{20} \\ $$$$=\mathrm{2}\left(\mathrm{5}×\mathrm{6}×\mathrm{7}×\mathrm{8}×\mathrm{9}×\mathrm{10}\right)=\frac{\mathrm{2}!\mathrm{10}!}{\mathrm{4}!} \\ $$

Commented by prakash jain last updated on 09/Jun/16

Thanks for the correction.

$$\mathrm{Thanks}\:\mathrm{for}\:\mathrm{the}\:\mathrm{correction}. \\ $$

Commented by Rasheed Soomro last updated on 09/Jun/16

I think 10×12×14×16×18×20 =2^6 ×(5.6.7.8.9.10)=((2^6 ×10!)/(4!)) =(((2!)^6 ×10!)/(4!))=(((2!)^(3!) ×10!)/(4!))

$${I}\:{think} \\ $$$$\mathrm{10}×\mathrm{12}×\mathrm{14}×\mathrm{16}×\mathrm{18}×\mathrm{20} \\ $$$$=\mathrm{2}^{\mathrm{6}} ×\left(\mathrm{5}.\mathrm{6}.\mathrm{7}.\mathrm{8}.\mathrm{9}.\mathrm{10}\right)=\frac{\mathrm{2}^{\mathrm{6}} ×\mathrm{10}!}{\mathrm{4}!} \\ $$$$\:\:\:\:\:\:\:\:=\frac{\left(\mathrm{2}!\right)^{\mathrm{6}} ×\mathrm{10}!}{\mathrm{4}!}=\frac{\left(\mathrm{2}!\right)^{\mathrm{3}!} ×\mathrm{10}!}{\mathrm{4}!} \\ $$

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