Basic Counting Principles: Practice

Fill the positions one at a time, and the choices shrink as each book is placed.

$3 \times 2 \times 1 = 6$

There are $3$ choices for the first spot, $2$ for the next, and $1$ for the last.

Each flip has $2$ outcomes, and the same $2$ choices repeat for all three flips, so multiply three twos.

$2 \times 2 \times 2 = 2^3 = 8$

You choose one trophy from two separate style groups (gold or silver), so add.

$3 + 5 = 8$

Multiplying would count gold-and-silver pairs, but only one trophy is ordered.

The code is a letter and then a digit, a sequence of two choices, so multiply.

$26 \times 10 = 260$

Place the students one position at a time, with the choices shrinking each step.

$4 \times 3 \times 2 \times 1 = 24$

Three independent choices in sequence, so multiply all three stage counts.

$2 \times 3 \times 2 = 12$

You pick one movie from two separate groups (a comedy or a drama), so add.

$6 + 4 = 10$

The $24$ from multiplying would count comedy-and-drama pairs, but you watch only one movie.

Each question has $2$ answers, and the $2$ choices repeat for both questions, so multiply.

$2 \times 2 = 2^2 = 4$

A flavor and a cone is a sequence of two choices, so multiply.

$4 \times 2 = 8$

You choose a single topping from two separate groups (vegetable or meat), so add.

$4 + 3 = 7$

A route is a road A-to-B and then a road B-to-C, a sequence of two choices, so multiply.

$3 \times 2 = 6$

Adding to get $5$ would answer a different question; the trip uses one road and then another.

Award gold first, then silver, with the choices shrinking.

$4 \times 3 = 12$

Any of $4$ swimmers can take gold, leaving $3$ who can take silver.