How many 4 digit nos that do not contain the digits 3 or 6 a : GMAT Problem Solving (PS)
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# How many 4 digit nos that do not contain the digits 3 or 6 a

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How many 4 digit nos that do not contain the digits 3 or 6 a [#permalink]

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02 Feb 2012, 03:46
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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 ?
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Re: How many 4 digit nos that do not contain the digits 3 or 6 a [#permalink]

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02 Feb 2012, 14:06
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 4 digit nos that do not contain the digits 3 or 6 a   [#permalink] 02 Feb 2012, 14:06
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