DarkHorse2019 wrote:
How many different three-digit integers have exactly three different digits?
(A) 504
(B) 648
(C) 720
(D) 891
(E) 1,000
Source: Math Bible (Jeff Sacksmann)
given: there are total of 10 digits (0,1,2,3,4,5,6,7,8,9)
thousands: 9 choices (because you can't have 0)
hundreds: 9 choices (10-1=9 digits left, since we used a digit for the thousands)
units: 8 choices (10-2=8 digits left, since we used a digit for the thousands and another for the hundreds)
total three-digit integers with different digits: 9*9*8=81*8=648
Answer (B).