Solve 48!/frac{(48-4)!{4!}}

$$\frac{ 48 ! }{ \frac{ (48-4) ! }{ 4 ! } }$$

Evaluate

$$112078080$$

Solution Steps

The factorial of 48 is 12413915592536072670862289047373375038521486354677760000000000.

$$\frac{12413915592536072670862289047373375038521486354677760000000000}{\frac{\left(48-4\right)!}{4!}}$$

Subtract 4 from 48 to get 44.

$$\frac{12413915592536072670862289047373375038521486354677760000000000}{\frac{44!}{4!}}$$

The factorial of 44 is 2658271574788448768043625811014615890319638528000000000.

$$\frac{12413915592536072670862289047373375038521486354677760000000000}{\frac{2658271574788448768043625811014615890319638528000000000}{4!}}$$

The factorial of 4 is 24.

$$\frac{12413915592536072670862289047373375038521486354677760000000000}{\frac{2658271574788448768043625811014615890319638528000000000}{24}}$$

Divide 2658271574788448768043625811014615890319638528000000000 by 24 to get 110761315616185365335151075458942328763318272000000000.

$$\frac{12413915592536072670862289047373375038521486354677760000000000}{110761315616185365335151075458942328763318272000000000}$$

Divide 12413915592536072670862289047373375038521486354677760000000000 by 110761315616185365335151075458942328763318272000000000 to get 112078080.

$$112078080$$

Factor

$$2^{8}\times 3^{4}\times 5\times 23\times 47$$