Combinations: If one has 5 different objects (e.g. A, B, C, D, and E), how many ways can they be grouped as 3 objects when position does not matter (e.g. ABC, ABD, ABE, ACD, ACE, ADE are correct but CBA is not ok as is equal to ABC) - answer is 10 ways. Formula: 5C3 = 5!/((5-3)!*3!) = 5*4*3*2*1/(2*1*3*2*1) = 5*2 = 10
Enter number of different objects ( 1 to 500 ):
Enter size of groups that can be taken from objects ( 1 to number above ):
For example, if we have 52 playing cards and are dealt a straight flush of the 10 and jack of spades, queen and king of hearts, and ace of diamonds, how often does this particular hand occur? To get the answer: enter 52 in the "number of different objects" box, enter 5 in the "size of groups" box, select "Combinations" from the radio buttons at top of screen and then click "Calculate Combinations" at the bottom.
The answer is 2598960 combinations or in other words, this hand occurs on average once in 2 million 598 hundred thousand 960 hands! Just as likely is a hand with the 8 of hearts, 3, 4 and jack of clubs, and 9 of spades (but you would not likely win at poker with this latter hand).