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how many different four digit numbers can be formed by rearranging the digits of 2010?
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Everything that does not start with "0" in the most left position.
It gives you 2*3*2*1 = 12 options.
And having two indistinguishable digits "0" forces you to divide 12 by 2! = 2.
In total, there are 
= 6 options. 6 numbers.
Answer. 6 numbers.
They are
2100 1200
2010 1020
2001 1002
