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How many 3-digit numbers satisfy the following conditions: The first d

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Bunuel
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How many 3-digit numbers satisfy the following conditions: The first d [#permalink] New post   18 Nov 2020, 04:11
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C
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83% (00:53) correct 17% (01:30) wrong based on 46 sessions
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How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and all digits are different from each other?

A. 504
B. 576
C. 648
D. 672
E. 810


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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. 504
B. 576
C. 648
D. 672
E. 810
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C
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CrackverbalGMAT
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Re: How many 3-digit numbers satisfy the following conditions: The first d [#permalink] New post   18 Nov 2020, 04:22
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Bunuel wrote:
How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and all digits are different from each other?

A. 504
B. 576
C. 648
D. 672
E. 810




There are 10 single digit numbers from 0 to 9.

The first digit can take any of the 9 digits from 1 to 9.

The 2nd digit can again take any 9 values (8 values remaining after the 1st digit is selected + 0)

The 3rd place can take any of the remaining 8 digits.

Total number of ways = 9 * 9 * 8 = 648


Option C

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How many 3-digit numbers satisfy the following conditions: The first d [#permalink] New post   18 Nov 2020, 04:37
Out of the 10 digits from 0 to 9,
the 1st digit (hundred’s place) can take any of the 9 digits from 1 to 9 (except 0)
The 2nd digit (ten’s place) can again take any 9 values (8 values remaining after the 1st digit is selected and 0)
The 3rd digit (unit’s place) can take any of the remaining 8 digits (barring the digits used at first two places)

Total number of ways = 9*9*8 = 648

Option C

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Re: How many 3-digit numbers satisfy the following conditions: The first d [#permalink] New post   18 Nov 2020, 09:58
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How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and all digits are different from each other?

Given:
The number is a 3 digit number
The first digit is different from zero
All digits are different from each other

Each digit of the 3 digit number can be any number from 0 - 9 (total 10 digits)

Digit in Hundred's place can we any digit from 1-9 = 9 options
Digit in ten's place can have any digit from 0 - 9 , except the digit in 100's place = 9 options
Digit in unit's place can have any digit from 0-9 except the 2 digits already in 10s and 100s = 8 options

Total possible numbers = 9*9*8 = 648

Ans: C
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Re: How many 3-digit numbers satisfy the following conditions: The first d [#permalink] New post   18 Nov 2020, 21:13
There is one condition in the first slot so we fill that one first.

Other than 0, there are 9 choices.

9 x 9 x 8 = 648

Answer: C
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Re: How many 3-digit numbers satisfy the following conditions: The first d [#permalink] New post   18 Nov 2020, 21:31
let the places be HTU
for H -> 9 ways
for T -> 9 remaining
and for U -> 8 remaining
so total = 9*9*8

that is
648

C is the answer
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Re: How many 3-digit numbers satisfy the following conditions: The first d [#permalink]
18 Nov 2020, 21:31
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