How many different three-digit numbers can be written using digits from the set $\{ 1,2,3,4,5 \}$ without any repeating digits?
A) 120
B) 10
C) 20
D) 60

Question

Quizplus · Accepted Answer

For a three-digit number without repeating digits, there are 5 choices for the first digit (since it can be any of the 5 numbers), 4 choices for the second digit (since one digit has already been used), and 3 choices for the third digit (since two digits have already been used). Multiplying these choices together gives $5 \times 4 \times 3 = 60$ different numbers.

How Many Different Three-Digit Numbers Can Be Written Using Digits {1,2,3,4,5}\{ 1,2,3,4,5 \}{1,2,3,4,5}

How Many Different Three-Digit Numbers Can Be Written Using Digits $\{ 1,2,3,4,5 \}$