How many hands in poker?

46 Views Asked by At

I guess the answer is pretty intuitive that its 52 C 4 to most people, but no one has been able to explain to me why it's not 52*51*50*49*48... My reasoning is the first time you choose you to have 52 cards to choose from, then 51, and so on and so on. Can someone please explain it to me?

1

There are 1 best solutions below

0
On BEST ANSWER

In this way you are overcounting the hands since for example the hand

  • A♦️K♦️Q♠️J♠️10 ♥️

  • K♦️Q♠️J♠️10 ♥️ A♦️

  • ...

is counted 5*4*3*2*1=5! and since this is true fir each hand we need to divide by 5! to obtain $\binom{52}{5}$ hands.