calculating the probabilities of each poker hand

There are 4! = 24 ways to arrange the people in the committee and 6! = 720 ways to arrange the others. However you don't have to establish an order of the people in the committee or those who aren't in the committee. You could consider the first four as the committee and the other six as the lucky ones. Why? For the example given there would be 10! = 3,628,800 ways to put the 10 people in your office in order. The general case is if you have to form a committee of y people out of a pool of x then there are x!/(y!*(x-y)!) combinations to choose from. How many different combinations of people are there to choose from? The answer is 10!/(4!*(10-4)!) = 210. The Combinatorial FunctionĪssume you want to form a committee of 4 people out of a pool of 10 people in your office. The total number of ways to arrange 52 cards would be 52! = 8.065818 * 10 67. Any scientific calculator should have a factorial button, usually denoted as x!, and the fact(x) function in Excel will give the factorial of x. If you had n cushions there would be n*(n-1)*(n-2)*. There are obviously 4 positions to put the first cushion, then there will be 3 positions left to put the second, 2 positions for the third, and only 1 for the last one, or 4*3*2*1 = 24.

How many combinations can you arrange them in? The answer is 4!, or 24. Let's assume your couch has four cushions.

The instructions for your living room couch will probably recommend that you rearrange the cushions on a regular basis. If you think 5! means to yell the number five then keep reading. If you already know about the factorial function you can skip ahead. The skills used here can be applied to a wide range of probability problems. This assumes some level mathematical proficiency anyone comfortable with high school math should be able to work through this explanation. I have been asked so many times how I derived the probabilities of drawing each poker hand that I have created this section to explain the calculation. On this page Poker Math Derivations for Five Card Stud

Calculating the probabilities of each poker hand