An arrangement of r objects, WITHOUT any regard to their ORDER and without repetition, selected from n distinct objects is called a combination of n objects taken r at a time. The number of such combinations is denoted by
The n and the r mean the same thing in both the permutation and combination; but the formula differs. Note that the combination has an extra r! in its denominator.
Combination means selection of things. The word selection is used when the order of things has no importance. The difference between combinations and permutations is that in combinations you are counting groups (order is not important) and in permutations you are counting different ways to arrange items by giving importance to order.
If 9 players are selected to form a team from 20 players, the order in which the 9 players are selected doesn’t matter as they are all in the team. This is combination. There will be a change in combination if a player in the team is changed.
A combination is a way to arrange items or numbers when order does not matter. Now you only have to figure out if the order does not matter. If you were to grab a yellow marble and a red marble from a bag of red and yellow marbles, order might not matter. As long as you draw two marbles, you don't need to pick the yellow first and the red second. Either way, you have both marbles. When order does not matter, it is a combination problem.
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Mathematics