How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
(a) 420
(b) 360
(c) 400
(d) 300
(b) 360
10 lakhs consists of seven digits.
Number of arrangements of seven numbers of which 2 are similar of first kind, 3 are similar of second kind $=\frac{7 !}{2 ! 3 !}$
But, these numbers also include the numbers in which the first digit has been considered as 0. This will result in a number less than 10 lakhs.
Thus, we need to subtract all those numbers.
Numbers in which the first digit is fixed as $0=$ Number of arrangements of the remaining 6 digits $=\frac{6 !}{2 ! 3 !}$
Total numbers greater than 10 lakhs that can be formed using the given digits $=\frac{7 !}{2 ! 3 !}-\frac{6 !}{2 ! 3 !}$
$=420-60$
$=360$
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