FORMULABANK

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Without replacement
If the number of combinations is without replacement, it means that the possibilities cannot be used more than once.

Example: Two balls are drawn from a bag containing three balls (green, blue, and red). This is without replacement.

Solution using a matrix and a tree diagram

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Solution by calculation:

3·2 = 6 possibilities (3 possibilities for drawing the first ball, but only 2 possibilities for drawing the second ball, since the first ball is not returned to the bag. Therefore, that ball cannot be drawn again).

As both the calculation, the matrix, and the tree diagram show, there are 6 possible combinations.

Note that, for example, the green ball cannot appear both times when two balls are drawn from the bag.