MAT-144 · Mathematical Reasoning Topic 07 · Taxes & Stocks
Topic 07 · Review · Q32

Counting principle

Identify the steps, count the choices per step, multiply across. The single most-used move in the topic. License plates, PINs, meals, passwords.

01 Worked Example Video

Every step of Counting principle explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE
02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

License plates (3 letters + 3 digits)

A license plate has 3 letters (from 26 letters) followed by 3 digits (0 through 9). Repeats allowed on both sides.

How many plates are possible?

total =
4-digit PIN

A bank PIN is 4 digits, each 0 through 9 with repeats allowed.

How many distinct PINs are possible?

total =
Restaurant meal combinations

A diner offers 5 appetizers, 8 entrees, 4 desserts. A meal is one of each. How many meals are possible?

total =
Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.
03 The Rule
total = n1 × n2 × … × nk product across independent steps
Each step’s count how many choices at that step
The counting principle powers half the topic. Break the process into independent steps, count the choices at each step, multiply across. License plates, PINs, meals, passwords, lottery tickets — same move every time.
Common slips
(1) Added instead of multiplied. 5 + 8 + 4 = 17 meals is wrong. The steps combine independently → 5 × 8 × 4 = 160. (2) Missed the “repeats allowed” clue. When repeats are allowed, each step has the full 10 (or 26) choices — not shrinking. (3) Confused with permutations. Counting principle with “no repeats” shrinks the numbers each step; that’s exactly the permutation formula in disguise.
04 Practice — Step by Step
Practice this problem step by step
A diner offers 4 appetizers, 6 entrees, and 3 desserts. A meal is one of each. How many different meals are possible?
Step 1

Add or multiply?

The meal is appetizer AND entree AND dessert. How do you combine the counts?
Step 2

Multiply the first two

Compute 4 × 6.
=
Step 3

Multiply by the dessert count

Now bring in the 3 desserts: 24 × 3.
total =
Q31 Q33
MAT-144 · TOPIC 07 · REVIEW · Q32 OF 38