Løs 52!/(52-25)!5!

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

Evaluer

$$61728305479136907531396158088806400000$$

Løsningsvejledning

Fakulteten af 52 er 80658175170943878571660636856403766975289505440883277824000000000000.

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

Subtraher 25 fra 52 for at få 27.

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

Fakulteten af 27 er 10888869450418352160768000000.

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

Fakulteten af 5 er 120.

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

Multiplicer 10888869450418352160768000000 og 120 for at få 1306664334050202259292160000000.

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

Divider 80658175170943878571660636856403766975289505440883277824000000000000 med 1306664334050202259292160000000 for at få 61728305479136907531396158088806400000.

$$61728305479136907531396158088806400000$$

Faktoriser

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