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The sum you require is 4!/2!2!, which is 6. This means there are 6 different two-digit numbers.

* * * * *

Wrong! The above formula is for the number of combinations, not permutations. However, since the number 23 is different from the number 32, you require permutations and not combinations.

There are 4*3 = 12

23, 25, 27,

32, 35, 37,

52, 53, 57,

72, 73, 75.

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