How many three-digit numbers can be made from the digits 0, 2, 4, 6 and 8 if no digit is used more than once in a number?

48Correct answerYour answer60Correct answerYour answer80Correct answerYour answer100Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The hundreds digit cannot be 0, so it has 4 choices.
The tens digit can be any of the remaining 4 digits (0 is now allowed).
The units digit has the remaining 3 choices, so the count is $4 \times 4 \times 3 = 48$ .

Worth noting

60 is $5 \times 4 \times 3$ , which lets 0 lead (giving two-digit 'numbers' like 024). 80 is $4 \times 5 \times 4$ , which forgets that the hundreds digit is already used when filling the tens place. 100 allows repetition.

Concept: Number formation when 0 cannot be the leading digit
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsThe counting principle

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Ten questions from Counting and Basic Probability, at your own pace.

How many three-digit numbers can be made from the digits 0, 2, 4, 6 and 8 if no digit is used more than once in a number?

Explanation