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count how many possible arrangement of 7 students lined up to be seated in a row of 2 chairs only?
This is a question about permutations. A permutation is an arrangement of a certain amount of objects in a specific order.
For example, if we have two people,
A
and
B
, we can arrange them in a row of two chairs in two ways
A
B
or
B
A
Each of these two arrangements is a permutation. Thus, there are only two possible permutations in the example.
If we have seven people it gets a bit trickier. We must use the multiplication principle.
If we have seven people and we want to know how many ways we can arrange them in a row of seven chairs, using the multiplication principle, we multiply all the options together to get the total number of arrangements. E.g. there are 7 options for the first seat, 6 for the second (because one has been used), 5 for the third, 4 for the fourth, and so on.
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