How many four-digit positive integers have digits that are all different and have both prime thousands and units digits?
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There actually are simple... 2,3,5, and 7 are the only prime digits, so you have four choices for the thousands and three choices for the units. The hundreds and tens can be any of the remaining 8 and 7 digits respectively. Therefore, there are 4*8*7*3=672 possible numbers.
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