TITLE: Special deck pair probability
QUESTION [3 upvotes]: I have a card deck having total $110$ cards. The deck has ten 10s, ten A's, ten J's, ten Q's, ten K's. How to compute the probability that if I turn five cards, I got at least one pair of 10, A, J, Q, or K?

REPLY [2 votes]: No court pair is the same as 0-5 singleton court cards.
$${60\choose 5}+{5\choose1}10{60\choose4}+{5\choose2}10^2{60\choose3}+...$$
{"set_name": "stack_exchange", "score": 3, "question_id": 1598130}