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How many five-digit numbers can be formed using the digits 5, 6, 7, 8, 9, 0 if no digits can be repeated

(A) 64 (B) 120 (C) 240 (D) 600 (E) 720

Take the task of creating 5-digit numbers and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select the first digit ASIDE: I say this is the most restrictive stage because the first digit CANNOT BE 0, otherwise the resulting number will not be a 5-digit (for example, 06785 is not a 5-digit number) The first digit can be 5, 6, 7, 8, or 9 So, we can complete stage 1 in 5 ways

Stage 2: Select the second digit There are 5 remaining digits from which to choose (since the digit 0 is now one of the options), so we can complete this stage in 5 ways.

Stage 3: Select the third digit There are 4 remaining digits from which to choose, so we can complete this stage in 4 ways.

Stage 4: Select the fourth digit We can complete this stage in 3 ways.

Stage 5: Select the fifth digit We can complete this stage in 2 ways.

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus create a 5-digit number) in (5)(5)(4)(3)(2) ways (= 600 ways)

Answer: D

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