Combinations: When Order Doesn’t Matter

A sports fan is deciding which of 6 baseball cards to be purchase. Two cards feature pitchers, two cards feature catchers and two feature outfielders. If the sports man plans to purchase 3 cards and decides that one card (and only one card) must be a pitcher, then how many combinations of baseball cards could he purchase (assume that the order of cards does not matter)?

(A) 9
(B) 12
(C) 18
(D) 20
(E) 30

There are two pitcher cards we can choose, so we just need to look at the Combination for how to choose the other 2 cards.

With the other 2 cards, we have 4 options (two catchers and two outfielders). Honestly, these numbers are so small, you could just count the options.

Let’s assign them each a letter:

ABCD —> AB, AC, AD, BC, BD, CD

There are six ways to choose the other 3 cards.

Those 6 ways x 2 possible pitches = 12. The correct answer is (B). Sometimes, the GMAT will take a hard concept and made it surprisingly easy!