Even Face Distribution

Count sequences using the multinomial coefficient, then divide by total sequences.

There are $6^{36}$ equally likely sequences of rolls.

1. 1. Count favorable sequences

   Number of sequences where each face appears exactly 6 times is the multinomial coefficient $\frac{36!}{(6!{)}^6}$.

2. 2. Total sequences

   Total possible sequences of 36 rolls is $6^{36}$.

3. 3. Probability

   Divide favorable by total.

   $$P=\frac{36!}{(6!{)}^6{6}^{36}}$$

Answer: 36! / ((6!)^6 * 6^36)