Selesaikan 52!/(52-25)!5!

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

Nilaikan

$$61728305479136907531396158088806400000$$

Langkah Penyelesaian

Faktorial 52 ialah 80658175170943878571660636856403766975289505440883277824000000000000.

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

Tolak 25 daripada 52 untuk mendapatkan 27.

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

Faktorial 27 ialah 10888869450418352160768000000.

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

Faktorial 5 ialah 120.

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

Darabkan 10888869450418352160768000000 dan 120 untuk mendapatkan 1306664334050202259292160000000.

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

Bahagikan 80658175170943878571660636856403766975289505440883277824000000000000 dengan 1306664334050202259292160000000 untuk mendapatkan 61728305479136907531396158088806400000.

$$61728305479136907531396158088806400000$$

Faktor

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