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MathNet 2008-part-02 — 165 problems (EN–VI) Question 62

Math Olympiad Vault · MathNet 2008-part-02 — 165 problems (EN–VI)

Question 62

A gang of thieves wants to open the safe of a bank. An insider got the bank manager drunk and managed to learn that:

a. the combination consists of 5 digits from 0 to 9;

b. the combination is an even number;

c. exactly one of the 5 digits of the combination is odd;

d. four different digits appear in the combination, the repeated digit is even and appears in two non-consecutive positions.

How many combinations are possible on the basis of this information?

(A) 3150
(B) 4500
(C) 5400
(D) 7200
(E) 9000