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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
