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How many four-digit numbers that do not contain the digits 3 or 6 are

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How many four-digit numbers that do not contain the digits 3 or 6 are [#permalink]

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New post 02 Feb 2012, 04:46
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How many four-digit numbers that do not contain the digits 3 or 6 are there?

A. 2401
B. 3584
C. 4096
D. 5040
E. 7200


Actual solution states that the first digit has 7 possibilities which excludes 0,3,& 6. And the other 3 digits have 8 possibilities. So the total possibilities are 7 * 8 * 8 * 8==3584. This solution is perfect but why can't the other 3 digits have deceasing possibilities. The first digit has 7 possibilities. The second digit has 8 possibilities. So after selecting the second digit the third digit can have only 7 possibilities. similarly 4th digit could have 6 possibilities.

Why can't this be possible ? Could someone please clarify ?
[Reveal] Spoiler: OA

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Re: How many four-digit numbers that do not contain the digits 3 or 6 are [#permalink]

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New post 02 Feb 2012, 15:06
abhi47 wrote:
How many 4 digit nos that do not contain the digits 3 or 6 are there ?

Actual solution states that the first digit has 7 possibilities which excludes 0,3,& 6. And the other 3 digits have 8 possibilities. So the total possibilities are 7 * 8 * 8 * 8==3584. This solution is perfect but why can't the other 3 digits have deceasing possibilities. The first digit has 7 possibilities. The second digit has 8 possibilities. So after selecting the second digit the third digit can have only 7 possibilities. similarly 4th digit could have 6 possibilities.

Why can't this be possible ? Could someone please clarify ?


Because we are not told that the digits must be distinct hence they can repeat.

If it were: "how many 4-digit numbers are there which do not contain 3 or 6 and have all distinct digits?" then the answer would be - 7*7*6*5. The first digit can tale 7 values (except 0, 3, and 6), the second digit can take also 7 values (except 3, 6 and the one we used for the first digit), and so on.

Hope it's clear.
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Re: How many four-digit numbers that do not contain the digits 3 or 6 are [#permalink]

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New post 07 Jun 2016, 08:03
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total numbers = 7*8*8*8 = 3584. Hence B.
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Re: How many four-digit numbers that do not contain the digits 3 or 6 are [#permalink]

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New post 07 Jun 2016, 09:22
Bunuel wrote:
How many four-digit numbers that do not contain the digits 3 or 6 are there?

A. 2401
B. 3584
C. 4096
D. 5040
E. 7200


1st Digit can be filled up by the numbers - { 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 7 ways

2nd Digit can be filled up by the numbers - { 0, 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways

3rd Digit can be filled up by the numbers - { 0, 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways

So, total No of ways is 7 * 8 * 8 => 3584

Hence answer will be (B)

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Re: How many four-digit numbers that do not contain the digits 3 or 6 are [#permalink]

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New post 18 Jul 2016, 03:55
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Bunuel wrote:
How many four-digit numbers that do not contain the digits 3 or 6 are there?

A. 2401
B. 3584
C. 4096
D. 5040
E. 7200


Bunuel,
How will the answer be different if the question asks about 4 digit number that does not contain the digits 3 and 6??

I started this question wrong by taking cases such as:Only 3 but not 6 and Only 6 but not 3.
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Re: How many four-digit numbers that do not contain the digits 3 or 6 are [#permalink]

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New post 07 Apr 2018, 10:02
Bunuel wrote:
How many four-digit numbers that do not contain the digits 3 or 6 are there?

A. 2401
B. 3584
C. 4096
D. 5040
E. 7200


Bunuel,
How will the answer be different if the question asks about 4 digit number that does not contain the digits 3 and 6??

I started this question wrong by taking cases such as:Only 3 but not 6 and Only 6 but not 3.

Exactly.. I also did it like this. There is clearly a difference b/w 3 or 6; 3 and 6.
Re: How many four-digit numbers that do not contain the digits 3 or 6 are   [#permalink] 07 Apr 2018, 10:02
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How many four-digit numbers that do not contain the digits 3 or 6 are

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