The first solution is to use the java.util.Random class:

import java.util.Random;

Random rand = new Random();

// Obtain a number between [0 - 49].
int n = rand.nextInt(50);

// Add 1 to the result to get a number from the required range
// (i.e., [1 - 50]).
n += 1;

Another solution is using Math.random():

double random = Math.random() * 49 + 1;

or

int random = (int)(Math.random() * 50 + 1);

Math.random() uses the Random class. And it's basically calling nextDouble() on the Random object of the Math class.

However the first method is definitely easier to understand and use. And has more options then the Math class has. So I'd go with the Random class if you need a lot of Random numbers or if you need types other then double. And I'd use Math.random() when you only need a double between 0 and 1.

So basically there is no difference in how the methods work, they both use the Random class. So wich of the two you use depends on the situation as I stated above.

From the javadoc for the Math class on the random method:

When this method is first called, it creates a single new pseudorandom-number generator, exactly as if by the expression

new java.util.Random()

Link to the javadoc page on Math.random(): https://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#random()

I hope this helps :)