# Combinations

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## 6/29 Combinations

As always, remember to follow the Knowsys method for math. Read the problem carefully and identify the bottom line (what you are looking for). Then, consider your options. How could you solve it? How should you solve it? There are usually several different ways to solve a problem. You should choose the method that gets you to the correct answer as quickly and reliably as possible. Next, attack the problem using the method that you have selected. Finally, loop back and verify that your answer matches the bottom line.

Cathy likes to wear 2 ribbons, each a different color. If she has 6 ribbons each of a different color, how many combinations of 2 different-colored ribbons can she select to wear?

This is a combination problem. If you have learned how to work combination problems it is very straightforward. You know that Cathy is selecting 2 ribbons out of 6 ribbons. When she selects the first ribbon, she has 6 different ribbons to choose from. When she selects the second ribbon, she has 5 ribbons to select from (since 1 of the ribbons has already been chosen). If this were a permutation problem, (in other words, if we cared if she chose a red ribbon first and then a blue ribbon or if she chose a blue ribbon first and then a red ribbon) then you would just multiply 6 and 5 and the correct answer would be 30. However, since you only care about which 2 ribbons she chooses (and not the order she chooses them in) you need to eliminate all the duplicates. There will be half as many different combinations as there are permutations so the final step is to divide 30 by 2. There are 15 different combinations of ribbons that Cathy can wear.

(A)  3
(B)  6
(C) 12
(D) 15
(E) 36

The correct answer choices is (D)

On sat.collegeboard.com 44% of the responses were correct.

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