Probability Question #9?

Question

All distinct arrangements of the letters "AAABBCCCDDDDEE" are placed in a bag and one is drawn at random.

What is the probability that it is AAABBCCCDDDDEE?

Answer 1

N = Number of distinct permutations

N = 14! / [(2!)²(3!)²(4!)]

Probability = 1 / N = [(2!)²(3!)²(4!)] / 14!

Answer 2

P(AAABBCCCDDDDEE) = 3!2!3!4!2!/14!
= 1/459098600