How many three-digit numbers are there such that all three digits are

Question

How many three-digit numbers are there such that all three digits are different and the first digit is not zero?

A. 504
B. 648
C. 720
D. 729
E. 810

robertsonsd · Accepted Answer

The first digit cannot be 0, so there are  9  options for the first digit.
the second digit can be any number (10 possibilities) but cannot be equal to the first digit. Therefore, there are (10-1)  9  possibilities for the 2nd digit.
The third digit can be any digit (10 possibilities) but cannot be equal to the first two digits. Therefore, there are (10-2)  8  possibilities for the 3rd digit.

So there are 9 * 9 * 8 = 648 possibilities.

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: 3digitnumbers_text.PNG

Lucky2783 · Answer

answer B

9*9*8

OptimusPrepJanielle · Answer

All three digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 8 ways. Total ways = 9*9*8 = 648 Hence option (B). -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

rhine29388 · Answer

hundreds digit can be placed in 9 ways
tens digit can be placed in 9 ways
units digit can be placed in 8 ways
total ways = 9*9*8 = 648 ways
correct answer - B

FB2017 · Answer

From arrangement concept we can have 9 combinations  * 9   * 8 
Option B.

AqsaGhori · Answer

for left most digit we can use any digit except zero so 
1 digit:9
2nd digit:9(Since now we can use 0 but couldnot used digit we used for hundreth place)
3rd digit:8(cannot use the digit we already used for ten and hundred) 
9*9*8
648
option B

apoorvasharma13 · Answer

Hi Bunuel.
If the question didn't specify "first digit is non-zero", will it make any difference to the answer? I don't think it will. But wanted to confirm.

Thanks,
Apoorva

MahmoudFawzy · Answer

Greetings  apoorvasharma13

sure won't make a difference.
it can be even confusing for who don't know whether the first digit is the first from the right or the first from the left.

(note: try tagging names to get the attention of specific user)

altairahmad · Answer

Will it not become 10x9x8 ?

Akhilesh38 · Answer

n general, there are 10 numbers that can be used for a digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Leftmost digit: However, since this digit cannot be zero, there are 10 - 1 = 9 possible options (the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9).

Middle digit: We can use 0 this time, but we cannot use the same number we picked for the leftmost digit. Thus, there are 10 - 1 = 9 possible options.

Rightmost digit: We cannot use either of the two numbers that we're already used, so there are 10 - 2 = 8 possible options.

9 x 9 x 8 = 648

Aakash25mn · Answer

How to calculate for even numbers ? (648 Divide by 2) ?

How many three-digit numbers are there such that all three digits are

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How many three-digit numbers are there such that all three digits are

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