Probability Question, need help

Question

I have 24 playing cards made up of 3 spades and 21 non-spades.

If I deal 8 cards each to three players, what is the probability that each player ends up with exactly one spade in his hand?

Answer 1

(8 choose 1)(8 choose 1)(8 choose 1)/(24 choose 3)

(24 choose 3) = 24*23*22/3*2 = 2024

8 choose 1 = 8

8*8*8/2024 = 512/2024 or just over 25%