The set of all k-combinations of a set S is sometimes denoted by ( S k ) {\displaystyle \textstyle {\binom {S}{k}}\,} . Combinations refer to the combination of n things taken k at a time without repetition.
https://en.wikipedia.org/wiki/Combination
In other words, how many different combinations of two pieces could you end up with? In counting combinations, choosing red and then yellow is the same as choosing yellow and then red because in both cases you end up with one red piece and one yellow piece.
http://onlinestatbook.com/2/probability/permutations.html
Combinations and Permutations Calculator. Find out how many different ways you can choose items. For an in-depth explanation of the formulas please visit Combinations and Permutations. Note: The old Flash version is here. For an in-depth explanation please visit Combinations and Permutations.
http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html
There are basically two types of permutation: 1  Repetition is Allowed: such as the lock above. It could be 333. 2  No Repetition: for example the first three people in a running race. You can't be first and second.
https://www.mathsisfun.com/combinatorics/combinations-permutations.html
There are also two types of combinations (remember the order does not matter now): 1  Repetition is Allowed: such as coins in your pocket (5,5,5,10,10) 2  No Repetition: such as lottery numbers (2,14,15,27,30,33)
https://www.mathsisfun.com/combinatorics/combinations-permutations.html
For example, a poker hand can be described as a 5-combination (k = 5) of cards from a 52 card deck (n = 52). The 5 cards of the hand are all distinct, and the order of cards in the hand does not matter. There are 2,598,960 such combinations, and the chance of drawing any one hand at random is 1 / 2,598,960.
https://en.wikipedia.org/wiki/Combination
More generally: choosing r of something that has n different types, the permutations are: n × n × ... (r times) (In other words, there are n possibilities for the first choice, THEN there are n possibilites for the second choice, and so on, multplying each time.)
https://www.mathsisfun.com/combinatorics/combinations-permutations.html
There are 720 different combinations for a seven-digit number. This answer can be found using the (n[n-1][[n-2] ... to k factors)/k!, where n is the possible number of digits and k is the number of digits in the number. For a seven-digit number, the formula is 10!/7!. Continue Reading.
https://www.reference.com/math/many-possible-combinations-seven-digit-number-2d752ca06d9fe3df
You are going to pick up these three pieces one at a time. The question is: In how many different orders can you pick up the pieces? Table 1 lists all the possible orders. There are two orders in which red is first: red, yellow, green and red, green, yellow. Similarly, there are two orders in which yellow is first and two orders in which green is first.
http://onlinestatbook.com/2/probability/permutations.html
In smaller cases it is possible to count the number of combinations. For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.
https://en.wikipedia.org/wiki/Combination
how many different combinations
There are 720 different combinations for a seven-digit number.