Question

she will buy 2filters, want to use now and the other to keep on hand at home. there are 6brands of filter she can choose from at the store. how many combinations of 2 different brands could she choose?

Answer 1

The student can choose from 15 different combinations of 2 different filter brands out of the 6 available at the store.

Step-by-step explanation:

To find out how many different combinations of 2 brands she can choose from 6, we use the formula for combinations without repetition, which is C(n, k) = n! / (k!(n-k)!), where 'n' is the total number of items to choose from, 'k' is the number of items to choose, '!' denotes factorial, and C(n, k) represents the number of combinations.

In this case, the student has 6 brands (n = 6) to choose from and wants to select 2 (k = 2). So we apply the combination formula:

• C(6, 2) = 6! / (2!(6-2)!) = (6 * 5 * 4 * 3 * 2 * 1) / ((2 * 1) * (4 * 3 * 2 * 1))
• Now we simplify the factorials: 6!/2!4! = (6 * 5) / (2 * 1) since the 4! in the numerator and denominator cancel out.
• Finishing the calculation gives us C(6, 2) = 15.

Therefore, the student can choose from 15 different combinations of 2 different brands of filters.