Problem 1855. Usage of java.math : N Choose K with unlimited precision

Calculate the binomial coefficient nchoosek with full accuracy. This challenge may use the wonderful word of java.math that allows unlimited precision calculations. The primary reference sites are Java Math, Java BigDecimal, and Java BigInteger.

The usage of BigDecimal functions add, multiply, and divide may be required.

Java Math:

vd-decimal value, vstr-string, vi-integer value 
xBD=java.math.BigDecimal(vd);  % valid vd,vstr,vi creates xBD a BigDecimal variable
import java.math.*;  % simplifies statements
xBD=BigDecimal(vstr);
xplusyBD=xBD.add(BigDecimal(y)); % add input requires BD type
xmultiplyzBD=xBD.multiply(BigDecimal(z));  % multiply input requires BD type
xdividezBD=xBD.divide(BigDecimal(z));  % divide input requires BD type
xmultydivz=xBD.multiply(yBD).divide(zBD);  out=x*y/z

To convert java to string of unlimited length can be achieved via java toString or Matlab char

xstr=toString(xBD)  or xstr=char(xBD) 

Input: [N,K] [ Inputs to nchoosek(N,K) 0<=K<=N<200 ]

Output: C (char variable of C=nchoosek(n,k) or BigDecimal variable type )

Theory:

C(n,k) link shows multiple evaluation methods.

C(n,k)= n!/(k!(n-k)!)

The factorial method gives a direct solution while the multiplicative may require fewer operations.

Hint: C(5,3)=(5/3)*(4/2)*(3/1)= (5/1)*(4/2)*(3/3); numerator has k terms

Future Challenges:

1. Usage of java.math

2. nchoosek_large (full precision)
3. Next Prime
4. factor_large

5. Factorial