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A 5-card hand is dealt from a well-shuffled deck of 52 playing cards. What is the probability that the hand contains at least one card from each of the four suits?

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  • $\begingroup$ Please edit your question to show what you have attempted and indicate where you are stuck. $\endgroup$ – N. F. Taussig Oct 11 '17 at 8:30
  • $\begingroup$ I typically try to post my attempted solutions to all of my math questions, but this one (and another I have posted just now) has me entirely stumped. Its an example from my notes that I just didn't get, so it is not a homework problem. I'll try to solve it, but based on what is in my notes (copied down from my professor), I entirely don't understand the process of solving it. $\endgroup$ – joe_04_04 Oct 11 '17 at 8:32
  • $\begingroup$ I think that it is a duplicate of this question. $\endgroup$ – M. P. Oct 11 '17 at 8:43
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Hint: Observe that if a five-card hand contains all four suits, it must contain two cards of one suit and one card from each of the other suits. Therefore, for the favorable cases, choose the suit from which two cards are drawn, choose two cards of that suit, choose one card from each of the other suits.

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