Problem:
How many four-digit numbers, N=abcdbase ten , satisfy all three of the following conditions?
(i) 4000≤N<6000;(ii) N is a multiple of 5;(iii) 3≤b<c≤6.
Answer Choices:
A. 10
B. 18
C. 24
D. 36
E. 48
Solution:
Condition (i) requires that a be one of the two digits, 4 or 5. Condition (ii) requires that d be one of the two digits, 0 or 5. Condition (iii) requires that the ordered pair (b,c) be one of these six ordered pairs:
(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)
Therefore, there are 2×2×6=24 numbers N satisfying the conditions.