Let's say you have 13 cards distributed from a standard deck, find the probability of this distribution of suits: 4, 4, 3, 2, (for instance 4 hearts, 4 clubs, 3 diamonds, 2 spades). My answer was:

$$\frac{ 4\*{13\choose 4} \* 3\*{13\choose 4} \* 2\*{13\choose 3} \* 1 \*{13\choose 2} }{52\choose 13}$$

My reasoning being that since there were 4 ways to choose the first suit, 3 ways to to choose the next etc... However the real answer was:

$$\frac{\frac{4!}2 \*{13\choose 4} \* {13\choose 4} \*2 \* {13\choose 3} \* {13\choose 2}}{52\choose 13}$$

Basically mine divided by 2, what I don't understand why the need to divide by 2. There are 4! ways the suits can be arranged, so why are they arranged in 4!/2 ways in the answer?