# How Many Numbers Greater than 10 Lacs Be Formed from 2, 3, 0, 3, 4, 2, 3 ?,420,360,400,300 - Mathematics

MCQ

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

• 420

• 360

• 400

• 300

#### Solution

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

Concept: Permutations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Q 4 | Page 46