you own 9 sweaters and are taking 3 on vacation. In how many ways can you choose 3 sweaters from the 9?
27
To find the number of ways you can choose 3 sweaters from 9, you can use the concept of combinations.
In general, the number of ways to choose k items from a set of n items is given by the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
Where "n!" denotes the factorial of n.
In this case, you want to find the number of ways to choose 3 sweaters from a set of 9, so the formula becomes:
C(9, 3) = 9! / (3! * (9 - 3)!)
Calculating this:
C(9, 3) = 9! / (3! * 6!) = (9 * 8 * 7) / (3 * 2 * 1) = 84
Therefore, there are 84 different ways you can choose 3 sweaters from the set of 9 sweaters.