ACT Arithmetic: Counting Methods

Frank has 8 hats, 5 scarves, and 4 pairs of gloves.  How many distinct outfits, each consisting of a hat, scarf, and pair of gloves, can Frank create?  

A.  17

B.  80

C.  160

D.  458

E.  480


Knowsys Method

Read the problem carefully.  

Identify the bottom line.   The number of distinct combinations = ? 

Assess your options.  You could start creating “outfits,” but we are looking at a large number so this will not be effective.  Let’s use what we know about counting methods.    

Attack the problem.  

Since an “outfit” consists of 1 of each item, the number of permutations will be:  8 x 5 x 4 = 160 (good thing we didn’t try to count them!)

The most common mistake here is adding (for answer A) rather than multiplying the options. 

Loop back.  Verify that you solved for the bottom line.

The correct answer is 160.  Pick C.

Level = Medium  

Want some help reviewing the math concepts you need to master?  Try these Knowsys resources:

  1. Knowsys Pre-Algebra Flashcards
  2. Knowsys Algebra I Flashcards
  3. Knowsys SAT & ACT Math Practice book.  

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