Untitled

public static void main(String[] args) {
		int n = 5, r = 2, p = 7; // output = 3

		// With Factorial Starts

		// Formula :: n!/ ( r! * (n-r)! )

		int nf = factorial(n);
		int rf = factorial(r);
		int nrf = factorial(n - r);

		int ansFact = (nf / (rf * nrf)) % p;

		System.out.println("Factorial :: " + ansFact);

		// With Factorial Ends

		// With Fast Power Starts

		// Formula :: (n! %p) * ((r ^ p-2) %p) * (( (n-r) ^ p-2) %p) )

		nf = factorial(n);
		rf = fastPower(r, p - 2, p);
		nrf = fastPower((n - r), p - 2, p);

		int ansFastpower = ((nf % p) * ((rf * nrf) % p));

		System.out.println("Fast Power :: " + ansFastpower);

		// With Fast Power Ends

	}

	private static int fastPower(int N, int Pow, int mod) {

		if (Pow == 0) {
			return 1;
		}
		if ((Pow & 1) == 1) {
			return ((N % mod) * (fastPower(((N * N) % mod), (Pow / 2), mod))) % mod;
		} else {
			return (fastPower(((N * N) % mod), (Pow / 2), mod));
		}
	}

	public static int factorial(int A) {

		if (A <= 1) {
			return 1;
		}

		return A * factorial(A - 1);
	}