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How many five-digit numbers can be formed using the digits 5

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How many five-digit numbers can be formed using the digits 5 [#permalink] New post 12 Sep 2017, 03:00
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Question Stats:

66% (01:07) correct 33% (32:08) wrong based on 3 sessions
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
[Reveal] Spoiler: OA

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Re: Combination [#permalink] New post 13 Sep 2017, 12:44
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pranab01 wrote:
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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Re: Combination   [#permalink] 13 Sep 2017, 12:44
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