jz92wjaz said:Second part is very close. I think you understand it but made a mistake when writing it down.
A combination is a selection of items from a larger set without any regard to the order in which the items are chosen. For example, choosing 3 toppings on a pizza from a list of 10 toppings would be considered a combination.
A combination does not consider the order of the items chosen, while a permutation does. For example, if we take the same pizza topping scenario, choosing pepperoni, mushrooms, and olives in that specific order would be a permutation, while choosing those same toppings in any order would be a combination.
The number of combinations depends on the number of items in the set and the number of items being chosen. The formula to calculate the number of combinations is nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items being chosen.
In a combination, each item can only be chosen once. Repetitions do not occur in a combination. For example, if we have a deck of cards and choose 5 cards, each card can only be chosen once, making it a combination.
Combinations are used in various fields such as mathematics, computer science, and statistics. In real life, combinations are used in scenarios where order does not matter, such as selecting a jury panel, assembling a team, or choosing a lottery ticket. They are also used in probability calculations and in coding algorithms.