Solve problems on the permutation of distinct objects without repetition

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

In how many ways can 2 of 5 different books be arranged in a row on a shelf?

Remember: The order matters here and nothing is used twice, so count the choices left for each place in turn.

Order matters and nothing repeats, so this is the permutation of 2 from 5.
5 × 4 = 20.
There are 20 ways.

Common mistakes

Used a combination. Here the order matters, so it is a permutation.
Multiplied the two numbers in the question. Count the choices left at each step.
Counted one place too few or too many. There is one factor for each place being filled.