How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
Question:

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

Solution:

(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 $=\frac{7 !}{2 ! 3 !}-\frac{6 !}{2 ! 3 !}$

$=420-60$

$=360$