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

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

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.

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