Lutasin ang 52!/(52-25)!5!

$$\frac{ 52 ! }{ (52-25) ! 5 ! }$$

I-evaluate

$$61728305479136907531396158088806400000$$

Mga Hakbang ng Solution

Ang factorial ng 52 ay 80658175170943878571660636856403766975289505440883277824000000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{\left(52-25\right)!\times 5!}$$

I-subtract ang 25 mula sa 52 para makuha ang 27.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{27!\times 5!}$$

Ang factorial ng 27 ay 10888869450418352160768000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{10888869450418352160768000000\times 5!}$$

Ang factorial ng 5 ay 120.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{10888869450418352160768000000\times 120}$$

I-multiply ang 10888869450418352160768000000 at 120 para makuha ang 1306664334050202259292160000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{1306664334050202259292160000000}$$

I-divide ang 80658175170943878571660636856403766975289505440883277824000000000000 gamit ang 1306664334050202259292160000000 para makuha ang 61728305479136907531396158088806400000.

$$61728305479136907531396158088806400000$$

I-factor

$$2^{23}\times 3^{9}\times 5^{5}\times 7^{5}\times 11^{2}\times 13^{2}\times 17^{2}\times 19\times 23\times 29\times 31\times 37\times 41\times 43\times 47$$