Consider the digits 1 - 9. They can be arranged in 9! ways. If you were to write down all of these possible arrangements on individual cards and then pick one, what is the possibility that the number you picked would be prime?
Answer:
Zero .......... In any nine-digit number using each of the digits once, the sum of the digits would be 45 (1+2+3+4+5+6+7+8+9 = 45). According to the rules of divisibility, any number in which the digits add up to a multiple of 9, is divisible by 9, and therefore not prime. Since 45 is a multiple of 9, the nine-digit number could not be prime.
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