java random string generation and birthday paradox

i need to write a random string generation class which generates 7char strings from a 31-char charset of numbers and some alphabets (10+26-5 , 5 vowels omitted). simple maths gives a set of 31^7 possible combinations ~ 27.5 billion. i have questions regarding the bday paradox, i ran some tests and the number of duplicates increase exponentially. can i do something to avoid this ?

At 1 million, duplicates encountered till now = 19
At 2 million, duplicates encountered till now = 69
At 3 million, duplicates encountered till now = 157
At 4 million, duplicates encountered till now = 280
At 5 million, duplicates encountered till now = 470
At 6 million, duplicates encountered till now = 662
At 7 million, duplicates encountered till now = 896
At 8 million, duplicates encountered till now = 1185
At 9 million, duplicates encountered till now = 1500
At 10 million, duplicates encountered till now = 1823
At 11 million, duplicates encountered till now = 2204
At 12 million, duplicates encountered till now = 2584
At 13 million, duplicates encountered till now = 3020
At 14 million, duplicates encountered till now = 3527
At 15 million, duplicates encountered till now = 4110
At 16 million, duplicates encountered till now = 4683
At 17 million, duplicates encountered till now = 5284
At 18 million, duplicates encountered till now = 5919
At 19 million, duplicates encountered till now = 6611
At 20 million, duplicates encountered till now = 7343
At 21 million, duplicates encountered till now = 8095
At 22 million, duplicates encountered till now = 8858
At 23 million, duplicates encountered till now = 9707
At 24 million, duplicates encountered till now = 10547
At 25 million, duplicates encountered till now = 11452
At 26 million, duplicates encountered till now = 12399
At 27 million, duplicates encountered till now = 13356
At 28 million, duplicates encountered till now = 14393
At 29 million, duplicates encountered till now = 15369
At 30 million, duplicates encountered till now = 16436

Below is the test class:

import java.util.Set;

import org.apache.commons.lang3.RandomStringUtils;

import com.google.common.collect.Sets;

public class RandomUnivmylocaL {

    public static void main(String[] argv) {

        final int million = 1_000_000;

        final int iterations = 30;
        // 31 chars
        final char[] charArr = new char[] { '1', '2', '3', '4', '5', '6', '7', 
                '8', '9', '0', 'B', 'C', 'D', 'F', 'G', 'H', 'J', 'K', 'L',
                'M', 'N', 'P', 'Q', 'R', 'S', 'T', 'V', 'W', 'X', 'Y', 'Z' };
        // System.out.println(charArr.length);

        final Set<String> set = Sets.newHashSetWithExpectedSize(
                iterations * million);

        for (int i = 0; i < iterations; i++) {
            for (int j = 0; j < million; j++) {
                final String univCode = RandomStringUtils.random(7, charArr);
                set.add(univCode);
            }
            System.out.println("At " + (i + 1) + " million, " +
                    "duplicates encountered till now = " + 
                    (((i + 1) * million) - set.size()));
        }
        System.out.println("done");
    }
}