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)?
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!