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A company plans to assign identification numbers to its empl [#permalink]
23 Aug 2008, 07:21

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Difficulty:

45% (medium)

Question Stats:

55% (01:47) correct
45% (00:43) wrong based on 318 sessions

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: PS: couting problem [#permalink]
23 Aug 2008, 07:34

2

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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?

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 _________________

Your attitude determines your altitude Smiling wins more friends than frowning

A company plans to assign identification numbers to its employees. Eac [#permalink]
09 Mar 2011, 21:08

1

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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]
09 Mar 2011, 21:20

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.

Re: A company plans to assign identification numbers to its empl [#permalink]
26 Feb 2013, 02:27

2

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Expert's post

1

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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.

Re: A company plans to assign identification numbers to its empl [#permalink]
23 Mar 2013, 07:28

1

This post received KUDOS

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?

Re: A company plans to assign identification numbers to its empl [#permalink]
23 Mar 2013, 07:52

1

This post received KUDOS

Expert's post

1

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mydreammba wrote:

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?

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]
31 Aug 2013, 04:50

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.

Re: A company plans to assign identification numbers to its empl [#permalink]
31 Aug 2013, 04:59

Expert's post

SUNGMAT710 wrote:

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.

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]
26 Nov 2014, 07:53

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]
10 Dec 2014, 19:52

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