Explanation:
To find the remainder when 1! 2! ... 95! is divided by 15, we need to calculate the sum of the remainders when each factorial is divided by 15 and then take the remainder of that sum when divided by 15.

Calculating the Remainders:
To calculate the remainder when a factorial is divided by 15, we can use the property of modular arithmetic that states a ≡ b (mod n) if and only if a - b is divisible by n.

Let's calculate the remainders for the factorials of numbers from 1 to 10:

1! ≡ 1 (mod 15)
2! ≡ 2 (mod 15)
3! ≡ 6 (mod 15)
4! ≡ 24 ≡ 9 (mod 15)
5! ≡ 120 ≡ 0 (mod 15)
6! ≡ 720 ≡ 0 (mod 15)
7! ≡ 5040 ≡ 15 (mod 15) ≡ 0 (mod 15)
8! ≡ 40320 ≡ 0 (mod 15)
9! ≡ 362880 ≡ 0 (mod 15)
10! ≡ 3628800 ≡ 0 (mod 15)

From the above calculations, we can observe that for factorials of numbers greater than or equal to 5, the remainder is always 0 when divided by 15.

Calculating the Remainder Sum:
Now, let's calculate the sum of the remainders for the factorials of numbers from 1 to 95:

1! + 2! + 3! + 4! + 5! + ... + 95!
≡ 1 + 2 + 6 + 9 + 0 + 0 + 0 + 0 + 0 + ... + 0 (mod 15)
≡ 18 (mod 15)
≡ 3 (mod 15)

Calculating the Final Remainder:
Finally, we take the remainder of the sum (3) when divided by 15:

3 ≡ 3 (mod 15)

Therefore, the remainder obtained when 1! 2! ... 95! is divided by 15 is 3. Therefore, the correct answer is option 'B'.