How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without…
How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?
Zero
One
Nine
Ten
Solution
The sum of the digits $1+2+3+4+5 = 15$, which is divisible by 3. Any number formed using all these digits will have digit sum 15 and hence be divisible by 3. Therefore no such five-digit number can be prime. The answer is zero.