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A company plans to assign identification numbers to its empl [#permalink]

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23 Aug 2008, 08:21

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A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

3024 4536 5040 9000 10000

= No. of ways select first digit (other than 0) * No of wasy select second digit (exclude first digit selected) * no of ways select 3rd digit (exclude first 2) * no of ways to select 4 th digit (excllude first 3 digits) = 9*9*8*6= 4536
_________________

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A company plans to assign identification numbers to its employees. Eac [#permalink]

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09 Mar 2011, 22:08

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A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

Re: A company plans to assign identification numbers to its employees. Eac [#permalink]

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09 Mar 2011, 22:20

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geisends wrote:

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

A)3,024 B)4,536 C)5,040 D)9,000 E)10,000

First digit (1000th place) can be any of 0 to 9 except 0, so it can be chosen in nine ways

Second digit (100th place) can be any of 0 to 9 except the one already chosen for 1000th place, so it can be chosen in nine ways

Third digit (10th place) can be any of 0 to 9 except the ones already chosen for 1000th place and 100th place, so it can be chosen in eight ways

Fourth digit (units place) can be any of 0 to 9 except the ones already chosen for 1000th place, 100th place and 10th place, so it can be chosen in seven ways

Total number of ways = 9*9*8*7 = 81*56. Only option with 6 in units place is B, so answer is B.

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

The first digit can take 9 values from 1 to 9 inclusive; The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0); The third digit can take 8 values; The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit of 6.

Re: A company plans to assign identification numbers to its empl [#permalink]

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23 Mar 2013, 08:28

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Bunuel wrote:

judokan wrote:

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

The first digit can take 9 values from 1 to 9 inclusive; The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0); The third digit can take 8 values; The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Answer: B.

Hope it's clear.

Hi Bunnel,

I took 9*10*10*10=9000 i thought he didn't mention any thing such as repetition not allowed or not allowed may i know if i misread the question?

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

The first digit can take 9 values from 1 to 9 inclusive; The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0); The third digit can take 8 values; The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Answer: B.

Hope it's clear.

Hi Bunnel,

I took 9*10*10*10=9000 i thought he didn't mention any thing such as repetition not allowed or not allowed may i know if i misread the question?

May i know where i went wrong?

"Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0"
_________________

Re: A company plans to assign identification numbers to its empl [#permalink]

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31 Aug 2013, 05:50

Bunuel wrote:

judokan wrote:

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

The first digit can take 9 values from 1 to 9 inclusive; The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0); The third digit can take 8 values; The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

The first digit can take 9 values from 1 to 9 inclusive; The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0); The third digit can take 8 values; The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Answer: B.

Hope it's clear.

why can't it be 9 * 10 * 10* 10 ?

Check the post just above yours: "Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0"
_________________

Re: A company plans to assign identification numbers to its empl [#permalink]

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26 Nov 2014, 08:53

When you start from the right hand side (from the 4th digit) you should get the same result but "magically" it doesn't. Can someone explain? What I mean is this: lets say the number is xyzt. t can take 10 digits, z can take 9 digits, y can take 8 digits and x can take 7-1=6 digits (deducting 1 for the "0" that it cannot take). The total number for probabilities is 10*9*8*6, which is different from 9*9*8*7. Can someone explain why we cannot do this version?

Re: A company plans to assign identification numbers to its employees. Eac [#permalink]

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10 Dec 2014, 20:52

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Re: A company plans to assign identification numbers to its empl [#permalink]

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08 Apr 2016, 10:59

Bunuel wrote:

judokan wrote:

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

The first digit can take 9 values from 1 to 9 inclusive; The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0); The third digit can take 8 values; The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit of 6.

Answer: B.

Hope it's clear.

I got the same answer almost but I multiplied it by 4! in the end assuming we could rearrange the digits and get a different number. Can you please explain why this is not correct?? Thank you.

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

The first digit can take 9 values from 1 to 9 inclusive; The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0); The third digit can take 8 values; The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit of 6.

Answer: B.

Hope it's clear.

I got the same answer almost but I multiplied it by 4! in the end assuming we could rearrange the digits and get a different number. Can you please explain why this is not correct?? Thank you.

The method used already takes care of all different arrangements. Try to test with smaller numbers to check.
_________________

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