15!*4!/18!

Let's simplify the expression:

\[ \frac{15! \times 4!}{18!} \]

Recall that:

\[ 18! = 18 \times 17 \times 16 \times 15! \]

So, substitute into the original expression:

\[ \frac{15! \times 4!}{18 \times 17 \times 16 \times 15!} \]

Cancel \( 15! \) from numerator and denominator:

\[ \frac{4!}{18 \times 17 \times 16} \]

Calculate \( 4! \):

\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

Now, compute the denominator:

\[ 18 \times 17 \times 16 \]

Let's multiply step by step:

• \( 18 \times 17 = 306 \)
• \( 306 \times 16 = 4,896 \)

Thus, the expression simplifies to:

\[ \frac{24}{4,896} \]

Divide numerator and denominator by 24:

\[ \frac{24 \div 24}{4,896 \div 24} = \frac{1}{204} \]

Final answer:

\[ \boxed{\frac{1}{204}} \]