Solve 59!/(59-2)!2!*0.01^2*0.99^59-2

$$\frac { 59 ! } { ( 59 - 2 ) ! 2 ! } \times 0.01 ^ { 2 } \times 0.99 ^ { 59 - 2 }$$

Evaluate

$$0.0964841780864035607342893773473177406890831814006065720940413468290417474383835953423801839901840786664275485562190989$$

Solution Steps

The factorial of 59 is 138683118545689835737939019720389406345902876772687432540821294940160000000000000.

$$\frac{138683118545689835737939019720389406345902876772687432540821294940160000000000000}{\left(59-2\right)!\times 2!}\times 0.01^{2}\times 0.99^{59-2}$$

Subtract 2 from 59 to get 57.

$$\frac{138683118545689835737939019720389406345902876772687432540821294940160000000000000}{57!\times 2!}\times 0.01^{2}\times 0.99^{59-2}$$

The factorial of 57 is 40526919504877216755680601905432322134980384796226602145184481280000000000000.

$$\frac{138683118545689835737939019720389406345902876772687432540821294940160000000000000}{40526919504877216755680601905432322134980384796226602145184481280000000000000\times 2!}\times 0.01^{2}\times 0.99^{59-2}$$

The factorial of 2 is 2.

$$\frac{138683118545689835737939019720389406345902876772687432540821294940160000000000000}{40526919504877216755680601905432322134980384796226602145184481280000000000000\times 2}\times 0.01^{2}\times 0.99^{59-2}$$

Multiply 40526919504877216755680601905432322134980384796226602145184481280000000000000 and 2 to get 81053839009754433511361203810864644269960769592453204290368962560000000000000.

$$\frac{138683118545689835737939019720389406345902876772687432540821294940160000000000000}{81053839009754433511361203810864644269960769592453204290368962560000000000000}\times 0.01^{2}\times 0.99^{59-2}$$

Divide 138683118545689835737939019720389406345902876772687432540821294940160000000000000 by 81053839009754433511361203810864644269960769592453204290368962560000000000000 to get 1711.

$$1711\times 0.01^{2}\times 0.99^{59-2}$$

Calculate 0.01 to the power of 2 and get 0.0001.

$$1711\times 0.0001\times 0.99^{59-2}$$

Multiply 1711 and 0.0001 to get 0.1711.

$$0.1711\times 0.99^{59-2}$$

Subtract 2 from 59 to get 57.

$$0.1711\times 0.99^{57}$$

Calculate 0.99 to the power of 57 and get 0.563905190452387847658032597003610407300310820576309597276688175505796302971265899137230765576762587179588244045699.

$$0.1711\times 0.563905190452387847658032597003610407300310820576309597276688175505796302971265899137230765576762587179588244045699$$

Multiply 0.1711 and 0.563905190452387847658032597003610407300310820576309597276688175505796302971265899137230765576762587179588244045699 to get 0.0964841780864035607342893773473177406890831814006065720940413468290417474383835953423801839901840786664275485562190989.

$$0.0964841780864035607342893773473177406890831814006065720940413468290417474383835953423801839901840786664275485562190989$$

Factor

$$\frac{29 \cdot 59 \cdot 3 ^ {114} \cdot 11 ^ {57}}{2 ^ {118} \cdot 5 ^ {118}} = 0.09648417808640355$$