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How many 3-digit numbers satisfy the following conditions:

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Senior Manager
Joined: 19 Nov 2007
Posts: 457

Kudos [?]: 223 [0], given: 4

How many 3-digit numbers satisfy the following conditions: [#permalink]

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05 Jan 2008, 14:17
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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.
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Kudos [?]: 223 [0], given: 4

Director
Joined: 12 Jul 2007
Posts: 857

Kudos [?]: 334 [0], given: 0

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05 Jan 2008, 15:32
There are 10 different integers available for us to use: 0,1,2,3,4,5,6,7,8,9

If the first digit is different from 0 we have 9 to choose from

Now they say the "other digits are different from each other" so the 2nd and 3rd can't be the same one, but one of them CAN be the same as the first digit. This gives us 10 choices for the 2nd digit and 9 choices for the third(since it cannot be identical to the second).

Options for first digit * options for second * options for 3 = number of 3 digit numbers that satisfy the conditions

9*10*9 = 810

Kudos [?]: 334 [0], given: 0

Re: PS-3 digit number   [#permalink] 05 Jan 2008, 15:32
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