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