Solve 100!/95!*5!*0.05^5*0.95^95+0.564

$$\frac { 100 ! } { 95 ! \times 5 ! } \times 0.05 ^ { 5 } \times 0.95 ^ { 95 } + 0.564$$

Evaluate

$$0.744017827270429150945185532599151455716177933247345457193892611957619921445464926496092373184410660585705696099545748533866430283228929429075876805649834323796998347688713693059980869293212890625$$

Solution Steps

The factorial of 100 is 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{95!\times 5!}\times 0.05^{5}\times 0.95^{95}+0.564$$

The factorial of 95 is 10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000\times 5!}\times 0.05^{5}\times 0.95^{95}+0.564$$

The factorial of 5 is 120.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000\times 120}\times 0.05^{5}\times 0.95^{95}+0.564$$

Multiply 10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000 and 120 to get 1239597418588687111511964251927367251447729560814084744305470068548115278511364374984611845046250936227593868423707192882049843200000000000000000000000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{1239597418588687111511964251927367251447729560814084744305470068548115278511364374984611845046250936227593868423707192882049843200000000000000000000000}\times 0.05^{5}\times 0.95^{95}+0.564$$

Divide 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 by 1239597418588687111511964251927367251447729560814084744305470068548115278511364374984611845046250936227593868423707192882049843200000000000000000000000 to get 75287520.

$$75287520\times 0.05^{5}\times 0.95^{95}+0.564$$

Calculate 0.05 to the power of 5 and get 0.0000003125.

$$75287520\times 0.0000003125\times 0.95^{95}+0.564$$

Multiply 75287520 and 0.0000003125 to get 23.52735.

$$23.52735\times 0.95^{95}+0.564$$

Calculate 0.95 to the power of 95 and get 0.0076514281153818492497108910522923939889608448570427803043646059567958108943618778356292728753731576478313833091931623635414286047187179783985819399826089348692903513438068330287933349609375.

$$23.52735\times 0.0076514281153818492497108910522923939889608448570427803043646059567958108943618778356292728753731576478313833091931623635414286047187179783985819399826089348692903513438068330287933349609375+0.564$$

Multiply 23.52735 and 0.0076514281153818492497108910522923939889608448570427803043646059567958108943618778356292728753731576478313833091931623635414286047187179783985819399826089348692903513438068330287933349609375 to get 0.180017827270429150945185532599151455716177933247345457193892611957619921445464926496092373184410660585705696099545748533866430283228929429075876805649834323796998347688713693059980869293212890625.

$$0.180017827270429150945185532599151455716177933247345457193892611957619921445464926496092373184410660585705696099545748533866430283228929429075876805649834323796998347688713693059980869293212890625+0.564$$

Add 0.180017827270429150945185532599151455716177933247345457193892611957619921445464926496092373184410660585705696099545748533866430283228929429075876805649834323796998347688713693059980869293212890625 and 0.564 to get 0.744017827270429150945185532599151455716177933247345457193892611957619921445464926496092373184410660585705696099545748533866430283228929429075876805649834323796998347688713693059980869293212890625.

$$0.744017827270429150945185532599151455716177933247345457193892611957619921445464926496092373184410660585705696099545748533866430283228929429075876805649834323796998347688713693059980869293212890625$$