Basic Counting Principles: Practice

One book is chosen from two separate groups (fiction or nonfiction), so add the group sizes.

$8 + 5 = 13$

Fill the five positions one at a time, with the choices shrinking each step.

$5 \times 4 \times 3 \times 2 \times 1 = 120$

Each of the three positions has $10$ choices, and the same $10$ choices repeat, so multiply three tens.

$10 \times 10 \times 10 = 10^3 = 1000$

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

$5 \times 4 = 20$

Any of $5$ athletes can take gold, leaving $4$ for silver.

Each flip has $2$ outcomes, repeated for all five flips, so multiply five twos.

$2 \times 2 \times 2 \times 2 \times 2 = 2^5 = 32$

Three independent choices in sequence, so multiply the three counts.

$3 \times 5 \times 2 = 30$

Fill the four positions one at a time, with the choices shrinking each step.

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

A route is a first road and then a second road, a sequence of two choices, so multiply.

$4 \times 3 = 12$

One scoop is chosen from two separate flavor groups (fruit or chocolate), so add.

$6 + 4 = 10$

Each question has $2$ answers, repeated for all four questions, so multiply four twos.

$2 \times 2 \times 2 \times 2 = 2^4 = 16$

A meal is a bread, a filling, and a drink, three independent choices in sequence, so multiply the three counts.

$3 \times 4 \times 3 = 36$

Fill the six positions one at a time, with the choices shrinking each step.

$6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$