Question 1208272
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The language used in the statement of the problem could definitely be better.<br>
On the surface, it sounds as if one of the digits is used twice and another of the digits is also used twice.<br>
But the wording says each of two different digits is "repeated twice".  Does that mean it is used THREE times? (used, then repeated, then repeated a second time = used three times)<br>
Assuming that the intended meaning is that each of two of the digits is used twice and a different digit is used once....<br>
(1) Choose the two digits to be used twice each in C(5,2) = 10 ways.
(2) Choose the digit to be used once in C(3,1) = 3 ways.
(3) Arrange the digits XXYYZ in (5!/((2!)(2!)) = 30 ways.<br>
ANSWER: 10*3*30 = 900<br>
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The almighty has spoken....<br>
tutor @ikleyn, who speaks perfect English (as evidenced by some of the things she writes in her posts!) has pronounced that "repeated twice" means the same thing as "used twice". So all of us lesser beings must accept that.<br>
Balderdash....!<br>
If you do something and then repeat it, you have done it twice.  If you repeat it again, then you have done it three times.<br>
So, with the problem as stated, each of two of the digits is used three times, which means the number must be at least 6 digits.  So, as tutor @Edwin says, the answer to the problem as stated is 0.<br>
If that was the intended meaning of the problem, then it is not a very interesting problem, or a good problem for a student to practice math on.<br>
So, instead of writing a lengthy response claiming that other tutors' responses are WRONG, I chose in my response to point out that one interpretation of the problem made the problem absurd, and to therefore assume that the intended meaning was that each of two of the digits is USED twice and another digit is used once.<br>