<s>[INST] Find the sum of all numbers greater than $10000$ formed by using all digits $0,1,2,4,5$ Find the sum of all numbers greater than $10,000$ formed by using all digits $0,1,2,4,5$ and no digit being repeated in any number.

I could find that the number of such numbers are $96$ but I could not find their sum.
 [/INST] Let's keep placeholders for where we will keep the digits :
[] [] [] [] []
Now, in the first box i.e: ten thousands place, we can put any number in the following set $ \{1,2,4,5 \}$ and after that have 4! ways of filling in the remaining numbers. So, there are 4! numbers with 1 as first number, 4! numbers with 2 as first number.. till 5. So, the sum of digits in ten thousand place is given as:
$$ 4!(1+2+4+5) \cdot 10^4$$
Similarly, suppose we fix some digit in the thousand place, then we have $ 3 \cdot 3!$ way of arranging the rest of numbers (remember we can't keep zero in first place). Hence the sum of no.s in thousand place is given as:
$$ 3 \cdot 3! ( 1 + 2 + 4 +5) \cdot 10^3$$
And, similar results for hundreds , tens and ones place. Now, to get the whole number, we just need to add up the parts of it's expanded form. Hence,
$$ \text{number}  = 4!(1+2+4+5) \cdot 10^4 + 3 \cdot 3! (1+2+4+5) \cdot 10^3 + 3 \cdot 3! (1+2+4+5) \cdot 10^2 + 3 \cdot 3! (1+2+4+5) \cdot 10^1 + 3 \cdot 3! (1+2+4+5) \cdot 10^0  = 3119976$$
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