Solve [75!/0!75!*(0.04)^0*(0.96)^75]+[75!/1!74!*(0.04)^1*(0.96)^74]

$$[ \frac { 75 ! } { 0 ! 75 ! } \times ( 0.04 ) ^ { 0 } \times ( 0.96 ) ^ { 75 } ] + [ \frac { 75 ! } { 1 ! 74 ! } \times ( 0.04 ) ^ { 1 } \times ( 0.96 ) ^ { 74 } ]$$

Evaluate

$$0.193092955901344880148690703293172713719141576314506455674208893522581493377668630183036624775387950588867878977788707292224837048253223000270151090176$$

Solution Steps

The factorial of 75 is 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000.

$$\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{0!\times 75!}\times 0.04^{0}\times 0.96^{75}+\frac{75!}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

The factorial of 0 is 1.

$$\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{1\times 75!}\times 0.04^{0}\times 0.96^{75}+\frac{75!}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

The factorial of 75 is 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000.

$$\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{1\times 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}\times 0.04^{0}\times 0.96^{75}+\frac{75!}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

Multiply 1 and 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000 to get 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000.

$$\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}\times 0.04^{0}\times 0.96^{75}+\frac{75!}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

Divide 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000 by 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000 to get 1.

$$1\times 0.04^{0}\times 0.96^{75}+\frac{75!}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

Calculate 0.04 to the power of 0 and get 1.

$$1\times 1\times 0.96^{75}+\frac{75!}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

Multiply 1 and 1 to get 1.

$$0.96^{75}+\frac{75!}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

Calculate 0.96 to the power of 75 and get 0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+\frac{75!}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

The factorial of 75 is 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{1!\times 74!}\times 0.04^{1}\times 0.96^{74}$$

The factorial of 1 is 1.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{1\times 74!}\times 0.04^{1}\times 0.96^{74}$$

The factorial of 74 is 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{1\times 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000}\times 0.04^{1}\times 0.96^{74}$$

Multiply 1 and 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000 to get 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000}\times 0.04^{1}\times 0.96^{74}$$

Divide 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000 by 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000 to get 75.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+75\times 0.04^{1}\times 0.96^{74}$$

Calculate 0.04 to the power of 1 and get 0.04.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+75\times 0.04\times 0.96^{74}$$

Multiply 75 and 0.04 to get 3.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+3\times 0.96^{74}$$

Calculate 0.96 to the power of 74 and get 0.0487608474498345656941138139629224024543286808875016302207598215966114882266839975209688446402494824719363330751991685081375851131952583334015533056.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+3\times 0.0487608474498345656941138139629224024543286808875016302207598215966114882266839975209688446402494824719363330751991685081375851131952583334015533056$$

Multiply 3 and 0.0487608474498345656941138139629224024543286808875016302207598215966114882266839975209688446402494824719363330751991685081375851131952583334015533056 to get 0.1462825423495036970823414418887672073629860426625048906622794647898344646800519925629065339207484474158089992255975055244127553395857750002046599168.

$$0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376+0.1462825423495036970823414418887672073629860426625048906622794647898344646800519925629065339207484474158089992255975055244127553395857750002046599168$$

Add 0.046810413551841183066349261404405506356155533652001565011929428732747028697616637620130090854639503173058879752191201767812081708667448000065491173376 and 0.1462825423495036970823414418887672073629860426625048906622794647898344646800519925629065339207484474158089992255975055244127553395857750002046599168 to get 0.193092955901344880148690703293172713719141576314506455674208893522581493377668630183036624775387950588867878977788707292224837048253223000270151090176.

$$0.193092955901344880148690703293172713719141576314506455674208893522581493377668630183036624775387950588867878977788707292224837048253223000270151090176$$

Factor

$$\frac{11 \cdot 2 ^ {222} \cdot 3 ^ {76}}{5 ^ {150}} = 0.1930929559013449$$