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

The correct option is 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 kid = $\frac{7!}{2!3!}$

But, these numbers also include the numbers in which the first digit has bene 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 arrangement 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