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by Rahul@gurome » Tue Nov 23, 2010 7:13 pm
In a 3 digit number, if the first digit is not zero, the hundreds place can be filled in 9 ways.
The tens place can be filled in 9 ways and the units place in 8 ways.

So we will have 9*9*8 = 648, 3 digit numbers whose all 3 digits are different and the first digit is not zero.

The correct answer is a.
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by goyalsau » Tue Nov 23, 2010 7:13 pm
danjuma wrote:How many 3 digit numbers are there such that all 3 digits are different and the first digit is not zero?

a. 648

b. 724

c. 436

d.632

e.728
We have 900 three digit numbers,
Its good to notice that we will have 3 cases in all
I) Where all the digits are different from Each other
II ) Where only two digits are same,
III ) all three digits are the same,


III ) all three digits are the same,

There will be only 9 numbers in which all the three digits are the same, 111, 222, ...... 999 in total 9 numbers


II ) Where only two digits are same, { from 100 to 199 }

100, 101, 110 to 119 ( except 111 ) in total 9 numbers , 121, 122, 131, 133, , ( 2 numbers in 120 to 129 ) , again ( 2 numbers in 130 to 139 ) ... so in total 8 * 2 = 16 numbers

in total 1 + 1 + 9 + 16 = 27

27 * 9( For all the series from 100 to 199, 200 to 299 ........ ) = 243 ( two digits numbers )

243 + 9 = 252 in all

900 - 252 = 648
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by goyalsau » Tue Nov 23, 2010 7:15 pm
Rahul@gurome wrote:In a 3 digit number, if the first digit is not zero, the hundreds place can be filled in 9 ways.
The tens place can be filled in 9 ways and the units place in 8 ways.

So we will have 9*9*8 = 648, 3 digit numbers whose all 3 digits are different and the first digit is not zero.

The correct answer is a.
Great Work,,,,,,,,,,,,,

I don't know when i will able to think like this.......... :(
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by blaster » Tue Nov 23, 2010 11:04 pm
Rahul@gurome wrote:In a 3 digit number, if the first digit is not zero, the hundreds place can be filled in 9 ways.
The tens place can be filled in 9 ways and the units place in 8 ways.

So we will have 9*9*8 = 648, 3 digit numbers whose all 3 digits are different and the first digit is not zero.

The correct answer is a.
why did you pick the "8" as a third number? i understand the hundreds digit must be 9, but not tens and unit digit.
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by Rahul@gurome » Tue Nov 23, 2010 11:37 pm
why did you pick the "8" as a third number? i understand the hundreds digit must be 9, but not tens and unit digit.
For hundreds place we can have the digits 1, 2, 3, 4, 5, 6, 7, 8, 9. These are 9 in number.
So we say that the hundreds place can be filled in 9 ways.
For the tens place we have the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 availabe and these are 10 in number but remember that 1 has already been selected for hundreds place and there has to be no repitition of digits. So we have to select from remaining 9.
Or the tens place can be filled in 9 ways.
Again for the units place, the digits availabe are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These are 10 in number, but again 1 has been selected for hundreds place and 1 for tens place and there has to be no repitition of digits.
So the units place can be filled in 10 - 2 = 8 ways.

So the total 3 digit numbers with all digits different and hundreds digit not being zero is 9*9*8 = 648.
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