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Question
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
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Solution
One million (1,000,000) consists of 7 digits.
We have digits 2, 3, 0, 3, 4, 2 and 3.
Numbers formed by arranging all these seven digits =\[\frac{7!}{2!3!}\]
But, these numbers also include the numbers whose first digit is 0.
This is invalid as in that case the number would be less than a million.
Total numbers in which the first digit is fixed as 0 = Permutations of the remaining 6 digits =\[\frac{6!}{2!3!}\]
Numbers that are greater than 1 million =\[\frac{7!}{2!3!}\] - \[\frac{6!}{2!3!}\]= 360
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