Problem:
All of David's telephone numbers have the form , where , , and are distinct digits and in increasing order, and none is either or . How many different telephone numbers can David have?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The last seven digits of the phone number use seven of the eight digits , so all but one of these digits is used. The unused digit can be chosen in eight ways. The remaining seven digits are then placed in increasing order to obtain a possible phone number. Thus there are possible phone numbers.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions