Probability of a certain result obtaioned by throwing an octahedron

Question

Assume having a fair octahedron. We throw it $93$ times and get the following results: $\{33;7;8;1;2;0;5;37\}$

The numbers represent how many times the die fell on side $1, 2,...., 8$.
What is the probability we got such a result?

Answer 1

Use multinomial distribution with $p_i = 1/8$, $n=93, n_1 = 33, n_2 = 7, n_3 = 8, n_4 = 1, n_5 = 2, n_6 = 0, n_7 = 5, n_8 = 37$ for i = 1 to 8. The required prob = $$\frac{93!}{33!\cdot7!\cdot8!\cdot1!\cdot2!\cdot0!\cdot5!\cdot37!}\cdot{(\frac{1}{8})}^{93}$$ http://en.wikipedia.org/wiki/Multinomial_distribution