Use the Combination Notation.
Here, the total number of sweaters is 5.
So, to find the number of sets of three sweaters that can be chosen, we have to find the number of combinations of 5 sweaters taken 3 at a time.
To find the number of combinations of
at a time, divide the number of permutations of
at a time by
Use the formula for permutations.
The number of permutations of
at a time can be written as
and evaluated using
Expand the factorials.
We know that
– 1) · (
– 2) · ... · 1.
5! = 5 · 4 · 3 · 2 · 1
2! = 2 · 1.
Divide out the common factors.
Divide out the common factors. So,
= 5 · 4 · 3.
Substitute 5 · 4 · 3 for
in equation (1).
Expand the factorial.
5 · 2 = 10
Therefore, you can choose 10 sets of three sweaters.
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