A combination is a way of selecting a group or subset of objects from a larger set, where the order of selection does not matter. For example, choosing three different colored marbles from a bag of five marbles would be a combination.
The number of combinations can be calculated using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects being selected.
The main difference between combinations and permutations is that permutations consider the order of objects, while combinations do not. In permutations, the order of selection matters, while in combinations it does not.
It depends on the problem. Sometimes repetitions are allowed in combinations, while other times they are not. For example, if you are choosing a combination of toppings for a pizza, you would not want to allow repetitions, but if you are choosing a combination of lottery numbers, repetitions would be allowed.
Combinations are used in many real-life scenarios, such as choosing a team from a group of players, selecting a jury from a pool of candidates, or creating a password using a combination of letters and numbers. They are also commonly used in statistics and probability to calculate the chances of certain outcomes.