There are 4^6 = 4096 such numbers.
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smallest=1234 greatest=4321
32 -(1+4) =27
1234 billion
There are 4 ways to chose the first digit. Then because there is to be no repetition, there are 3 ways to choose the second. This means that there are 4 x 3 ways of setting down the first two digits 12 _ _ 13 _ _ 14 _ _ 21 _ _ 23 _ _ 24 _ _ 31 _ _ 32 _ _ 34 _ _ 41 _ _ 42 _ _ 43 _ _ .... now you can take it from there.
a 8-digits palindromic number is a number consisting of a 4-digits number written and then written backward, i.e. 1234 4321 so there are as many palindromic 8-digits numbers as 4-digits numbers so from 1000 to 9999, so there are 8999 palindromic 8 digits number (I assumed that 00011000 is not to be considered as a valid 8 digit number)