Solve 40!/35!*5!/frac{50!{45!*5!}}

$$\frac { \frac { 40 ! } { 35 ! \cdot 5 ! } } { \frac { 50 ! } { 45 ! \cdot 5 ! } }$$

Evaluate

$$\frac{82251}{264845}\approx 0.310562782$$

Solution Steps

Divide \frac{40!}{35!\times 5!} by \frac{50!}{45!\times 5!} by multiplying \frac{40!}{35!\times 5!} by the reciprocal of \frac{50!}{45!\times 5!}.

$$\frac{40!\times 45!\times 5!}{35!\times 5!\times 50!}$$

Cancel out 5! in both numerator and denominator.

$$\frac{40!\times 45!}{35!\times 50!}$$

The factorial of 40 is 815915283247897734345611269596115894272000000000.

$$\frac{815915283247897734345611269596115894272000000000\times 45!}{35!\times 50!}$$

The factorial of 45 is 119622220865480194561963161495657715064383733760000000000.

$$\frac{815915283247897734345611269596115894272000000000\times 119622220865480194561963161495657715064383733760000000000}{35!\times 50!}$$

Multiply 815915283247897734345611269596115894272000000000 and 119622220865480194561963161495657715064383733760000000000 to get 97601598220200855406862080626319653687095027127240868009509734628173016946912757022720000000000000000000.

$$\frac{97601598220200855406862080626319653687095027127240868009509734628173016946912757022720000000000000000000}{35!\times 50!}$$

The factorial of 35 is 10333147966386144929666651337523200000000.

$$\frac{97601598220200855406862080626319653687095027127240868009509734628173016946912757022720000000000000000000}{10333147966386144929666651337523200000000\times 50!}$$

The factorial of 50 is 30414093201713378043612608166064768844377641568960512000000000000.

$$\frac{97601598220200855406862080626319653687095027127240868009509734628173016946912757022720000000000000000000}{10333147966386144929666651337523200000000\times 30414093201713378043612608166064768844377641568960512000000000000}$$

Multiply 10333147966386144929666651337523200000000 and 30414093201713378043612608166064768844377641568960512000000000000 to get 314273325316763267926595272318605593619028126825377292531137684254276333093884683878400000000000000000000.

$$\frac{97601598220200855406862080626319653687095027127240868009509734628173016946912757022720000000000000000000}{314273325316763267926595272318605593619028126825377292531137684254276333093884683878400000000000000000000}$$

Reduce the fraction \frac{97601598220200855406862080626319653687095027127240868009509734628173016946912757022720000000000000000000}{314273325316763267926595272318605593619028126825377292531137684254276333093884683878400000000000000000000} to lowest terms by extracting and canceling out 1186631143939901708269347249593556962068485819348589901758151689683687942358302720000000000000000000.

$$\frac{82251}{264845}$$

Factor

$$\frac{3 ^ {2} \cdot 13 \cdot 19 \cdot 37}{5 \cdot 7 ^ {2} \cdot 23 \cdot 47} = 0.3105627820045687$$