Anne, Joe and Lynn, in this order, will take turns to draw two cards from a standard deck of 52 cards. Note that each draw of 2 cards is w/o replacement but draws of different turns are with replacement (the preceding two cards will be put back and the deck will be reshuffled.) If they will take turns until four suit matches (two cards of the same suit) are observed what is the probability that each of them will take five turns.

Question

Anne, Joe and Lynn, in this order, will take turns to draw two cards from a standard deck of 52 cards.  Note that each draw of 2 cards is w/o replacement but draws of different turns are with replacement (the preceding two cards will be put back and the deck will be reshuffled.)  If they will take turns until four suit matches (two cards of the same suit) are observed what is the probability that each of them will take five turns.