To find the number of 6-digit numbers of the form ababab in base 10 that are products of exactly 6 distinct primes, you can use the following approach:
First, consider the 6 prime numbers that can be used to form the 6-digit number. There are 6 choices for the first digit (a), 5 choices for the second digit (b), 4 choices for the third digit (a), 3 choices for the fourth digit (b), 2 choices for the fifth digit (a), and 1 choice for the sixth digit (b). This gives a total of 6 * 5 * 4 * 3 * 2 * 1 = 720 possible 6-digit numbers.
However, not all of these numbers will be of the form ababab. To ensure that the number is of this form, the first and fourth digits must be the same, and the second and fifth digits must be the same. This means that there are 2 choices for the first digit (either a or b), and 1 choice for the second digit (either a or b). Therefore, there are a total of 2 * 1 = 2 ways to arrange the digits to form a 6-digit number of the form ababab.
Therefore, the total number of 6-digit numbers of the form ababab in base 10 that are products of exactly 6 distinct primes is 720 / 2 = 360.
Thus, the answer is (3) 13.