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help :(

by sana.noor » Tue Jul 23, 2013 9:22 am
How many 4-digit numbers can be formed by using the digits 0-9, so that the numbers contains exactly 3 distinct digits?

(A) 1944
(B) 3240
(C) 3850
(D) 3888
(E) 4216

OA is D
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by sana.noor » Tue Jul 23, 2013 9:26 am
I knwo 0 cant be the first digit so 9 chances for the first digit, 9 chances for the second digit because now we can add 0 and 8 chances for the thrid digit.
so it should be 9.9.8 = 648... i cant do the next step
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by GMATGuruNY » Tue Jul 23, 2013 10:09 am
How many 4 digit numbers can be formed by using the digits 0-9 so that it contains exactly 3 distinct digits?
(A)1944
(B)3240
(C)3850
(D)3888
(E)4216
Case 1: Tens digit and units digit the same:
Number of options for the thousands digit = 9. (Any digit 1-9)
Number of options for the hundreds digit = 9. (Any digit 0-9 not yet chosen)
Number of options for the tens digit = 8. (Any digit 0-9 not yet chosen)
Number of options for the units digit = 1. (Must be the same as the tens digit)
To combine the options above, we multiply:
9*9*8*1 = 648.

Other cases:
Of the 4 digits, any pair could be the two that are the same.
Number of combinations of 2 that can be formed from 4 options = 4C2 = 6.

To combine the options above, we multiply:
648*6 = 3888.

The correct answer is D.
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by vipulgoyal » Tue Jul 23, 2013 11:14 pm
Consider one case: Tens digit and units digit are the same:

Number of options for the thousands digit = 9. (Any digit 1-9)
Number of options for the hundreds digit = 9. (Any digit 0-9 not yet chosen)
Number of options for the tens digit = 8. (Any digit 0-9 not yet chosen)
Number of options for the units digit = 1. (Must be the same as the tens digit)
To combine the options above, we multiply:
9*9*8*1 = 648.

Other cases:
#ways if the HUNDREDS digit and the UNITS digit are the same (9*9*8*1)
#ways if the THOUSANDS digit and the UNITS digit are the same (9*9*8*1)
#ways if the HUNDREDS digit and the TENS digit are the same (9*9*1*8)
#ways if the THOUSANDS digit and the TENS digit are the same (9*9*1*8)
#ways if the THOUSANDS digit and the HUNDREDS digit are the same (9*1*9*8)

Total #ways = 648*6 = 3888.

Out of the 4 digits, any 2 have to be the same.
Number of ways this is possible: 4C2 = 6.
name unit,tens,hundred,thousand digit"s positions 4,3,2,1
now (1,2) (1,3) (1,4) (2,3) (2,4) (3,4) Can be same, 1,4 and 4,1 are same thats why combination is used
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