Four-letter codes are made from the letters of the word PENCIL, with no letter used twice. How many of these codes begin with a vowel?

Explanation

1. 01

   The vowels in PENCIL are E and I, so the first letter has 2 choices.

2. 02

   The other three places are filled from the remaining 5 letters: $5 \times 4 \times 3 = 60$.

3. 03

   Codes $= 2 \times 60 = 120$.