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

Answer 1

(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