Cards Probability help

Question

In the game of poker, five cards are dealt. Recall the regular deck of cards has 13 denominations and 4 suits.

What is the probability of getting 5 consecutive cards (i.e., from 2,3,4,5,6, all the way to 10,J,Q,K,A), all of the

same suit?

The answer to this problem is (9*4)/ 52 5)

I don't understand where the 9 is coming from and why its multiplied by 4 and generally what exactly the question is asking me. I also don't fully understand how to take what I know from the question and put it into an expression for me to solve. What things should I keep in mind to help me solve these types of questions correctly and put the information in the given question into math?

I know that the sample space is (52 5) but the rest I don't understand. Is it asking for consecutive number cards only?

Answer 1

In order to find the probability, find the number of ways you can get a straight flush and divide by the total ways you can get 5 cards out of 52.

There are 10 straights in a suit 1 to 5 up to 10 through A. The number is 10, not 9 because they did not specify a "straight flush" (you might not count the royal flush). Maybe they didn't consider an ace as both first card or fourteenth. Oh, I see that they started the count (incorrectly for poker) at 2 - so 9 straights of one suit. You can point this out in the HW and be a local hero...or universally despised.

So there are only 4*9 ways to get straight flushes as defined. (This is true in poker as well, but because of the Royal Flush exception - especially video poker, that actually treats RF as a hand with a different payout)

So P is 36/₅₂C₅

Please consider a tutor. Take care.