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how do you determine if a situation involves combination

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Rylai04id

Answer:

Step-by-step explanation:

A combination is a selection of things from a possible pool or group such that the order at which they are selected does not matter.

First, combinations deals with counting a selection of things. Problems involving selecting things give out a hint of permutation or combination. Selecting things often come word problems like picking up balls from a box, picking students in a class etc.

What separates permutation from combination is that in combination, the order at which things are selected does not matter. This is important as some problems do not clearly state when order does not matter.

In a combination problem, the important thing is whether something is picked or not (vs. the order). If the order at which something is picked is important, the problem deals with permutation. Usually, if there are specific things associated with the order of picking, those are permutations and not combination.

  • For example, choosing 3 students to form a "cleaners" group in a class deals with combination. That is because there is no importance to the order at which students are chosen. Student A, Student B, and Student C are picked in that order. That is the same thing as Student B, Student C, and Student A getting picked. It is still the same group of students.

  • In contrast, choosing officers, President, Vice President and Secretary from a class deals with permutation. Student A becoming a president, Student B becoming a VP, and Student C becoming a secretary is different from Student B getting the president, Student C becoming VP and Student A becoming the secretary. It is still the same group of students, but what they got are different. What they got are specified and therefore do not fall in combination.

Also, picking more than 1 thing at the same time is also a combination. Since there is no order at which the things are picked, it is automatically assumed as a combination. For example, drawing 4 balls in a box full of n amount of balls is a combination problem.

The formula for taking r things from a pool of n possible ones, with no regards to order is given by the formula:

[tex]\frac {n!}{r!(n-r!)}[/tex]

For more information about combinations, click here.

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