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Question Number 157329 by MathsFan last updated on 22/Oct/21

$$\mathit{w}\mathit{h}\mathit{a}\mathit{t}\mathit{s}\mathit{t}\mathit{h}\mathit{e}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{o}\mathit{f}$$$$!5$$

Answered by puissant last updated on 24/Oct/21

$$!5=5!(\frac{1}{0!}-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{120})=5!(\frac{1}{2}-\frac{1}{6}+\frac{1}{24}-\frac{1}{120})$$$$=5!(\frac{60}{120}-\frac{20}{120}+\frac{5}{120}-\frac{1}{120})=120\times \frac{44}{120}=44..$$

Commented by MathsFan last updated on 22/Oct/21

$$thankyousir$$$$canthisalsobetheanswer\left(\frac{5!}{e}\right)=44.146$$

Commented by puissant last updated on 22/Oct/21

$$yesss\left(\frac{5!}{e}\right)=\left(\frac{120}{e}\right)=44,14$$

Commented by puissant last updated on 22/Oct/21

Commented by MathsFan last updated on 22/Oct/21

$$thankyousenior$$

Commented by puissant last updated on 22/Oct/21

$$Derien..$$

Commented by MathsFan last updated on 22/Oct/21

$$mercibeaucoup$$😊

Answered by soumyasaha last updated on 22/Oct/21

$$=\mathrm{Subfactorial}5[\mathrm{No}.\mathrm{of}\mathrm{derangement}]$$$$$$$$=\lfloor \frac{5!}{\mathrm{e}}+\frac{1}{2}\rfloor$$$$=\lfloor 44.146+0.5\rfloor$$$$=\lfloor 44.646\rfloor$$$$=44$$

Commented by MathsFan last updated on 22/Oct/21

$$thankyousir$$$$butdoesthatmeanthequestionhas$$$$nouniquesolutionplease?$$

Commented by mr W last updated on 23/Oct/21

$$thereisuniquesolution!$$$$!5=44$$

Commented by mr W last updated on 23/Oct/21

Commented by MathsFan last updated on 25/Oct/21

$$thanksverymuch$$

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