Give your problem a cool name

Luke the Cat (me) wants to create a problem. However, he doesn't know what name to give the problem. Given that he can only use 26 letters in the alphabet, what are the chances that Luke the Cat would get the word "cool" on the first try? Note: Your answer would be in the form $\frac{a}{b}$ in the simplest form. Give your answer as $a + b$ . Also, Luke the Cat always tries 4 letters for the name of the problem.

Thanks to Yuxuan for helping me use latex