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A grandmother, mother, and daughter wish to arrange themselves in a row in order to be photographed. How many different ways can they arrange themselves?
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Let us regard the person on the right as the first in the set, the person in the middle as the second, and the person on the left as the third. The question is then: How many possible arrangements are there of the grandmother, mother and daughter? The grandmother, mother, and daughter can be considered a set of 3 items. Thus, the number of possible arrangements for this set is $3 !=3 \cdot 2 \cdot 1=6$. The possible arrangements are: grandmother-mother-daughter, grandmotherdaughter-mother, mother-grandmother-daughter, mother-daughter-grandmother, daughtergrandmother-mother, daughter-mother-grandmother.
by Diamond (88,180 points)

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