30!/29!2!

To simplify the expression \( \frac{30!}{29! \cdot 2!} \), we can use the property of factorials that states \( n! = n \times (n-1)! \).

So, first we can rewrite \( 30! \):

\[ 30! = 30 \times 29! \]

Now substituting this into the original expression gives us:

\[ \frac{30!}{29! \cdot 2!} = \frac{30 \times 29!}{29! \cdot 2!} \]

The \( 29! \) in the numerator and the denominator cancels out:

\[ = \frac{30}{2!} \]

Now we can compute \( 2! \):

\[ 2! = 2 \times 1 = 2 \]

Thus, we can further simplify the expression:

\[ = \frac{30}{2} = 15 \]

Therefore, the final result is:

\[ \boxed{15} \]