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# Combinations - how many 3 digit numbers?

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Intern
Joined: 17 Feb 2008
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Combinations - how many 3 digit numbers? [#permalink]  03 Mar 2009, 16:33
00:00

Difficulty:

(N/A)

Question Stats:

83% (01:11) correct 17% (00:52) wrong based on 6 sessions
4. How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and the other digits are all different from each other?

a) 648.
b) 504.
c) 576.
d) 810.
e) 672.

------------------------------------------------------------------------
- I have 9 x 8 x 7 = 504, but then also think it can be
9 x 9 x 8 = 648?
Confused ?
JF
Manager
Joined: 17 Dec 2008
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Re: Combinations - how many 3 digit numbers? [#permalink]  03 Mar 2009, 17:24
sHould be $$9x9x8 = 648.$$
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Re: Combinations - how many 3 digit numbers? [#permalink]  03 Mar 2009, 18:54
Forrester300 wrote:
4. How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and the other digits are all different from each other?

a) 648.
b) 504.
c) 576.
d) 810.
e) 672.

------------------------------------------------------------------------
- I have 9 x 8 x 7 = 504, but then also think it can be
9 x 9 x 8 = 648?
Confused ?
JF

This should be correct: 9 x 9 x 8 = 648.

The 3 digit integers are in xyz form: xyz

1: In x's place 1, 2, 3, 4, 5, 6, 7, 8, and 9 can be placed: so 9 ways
2: In y's place 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, but except x, can be placed: 9 ways
3: In z's place 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, but except x and y, can be placed: 8 ways

So, it is; 9 x 9 x 8 = 648.
_________________
Manager
Status: Preparing Apps
Joined: 04 Mar 2009
Posts: 91
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31
GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)
Followers: 1

Kudos [?]: 131 [0], given: 4

Re: Combinations - how many 3 digit numbers? [#permalink]  06 Mar 2009, 07:58
How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and the other digits are all different from each other?

a) 648.
b) 504.
c) 576.
d) 810.
e) 672.

If xyz is the number then, doesnt " the other digits " mean y & z?
IMO it should be 9 * 10 * 9 = 810.

Whats the OA??
Retired Moderator
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Re: Combinations - how many 3 digit numbers? [#permalink]  28 Mar 2010, 04:00
aalriy wrote:
How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and the other digits are all different from each other?

a) 648.
b) 504.
c) 576.
d) 810.
e) 672.

If xyz is the number then, doesnt " the other digits " mean y & z?
IMO it should be 9 * 10 * 9 = 810.

Whats the OA??

This is exactly what I thought! "Other digits" is creating ambiguity here. I thought that the last two digits should be different from each other. So I got 810
_________________
Re: Combinations - how many 3 digit numbers?   [#permalink] 28 Mar 2010, 04:00
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