How many numbers greater than 10 lakh can be | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) number greater than $10$ lakh must have at least $7$ digits.Since we have exactly $7$ digits $(2, 3, 0, 3, 4, 2, 3)$,any $7$-digit number formed u

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(B) number greater than $10$ lakh must have at least $7$ digits.Since we have exactly $7$ digits $(2, 3, 0, 3, 4, 2, 3)$,any $7$-digit number formed using these will be greater than $10$ lakh,provided the first digit is not $0$.The total number of permutations of these $7$ digits ($2$ appears twice,$3$ appears thrice,$0$ appears once,$4$ appears once) is given by $\frac{7!}{2! 	imes 3!} = \frac{5040}{2 	imes 6} = 420$.The number of permutations starting with $0$ (which are $6$-digit numbers) is $\frac{6!}{2! 	imes 3!} = \frac{720}{2 	imes 6} = 60$.Therefore,the number of $7$-digit numbers greater than $10$ lakh is $420 - 60 = 360$.

How many numbers greater than $10$ lakh can be formed using the digits $2, 3, 0, 3, 4, 2, 3$?

Similar Questions

If all permutations of the letters of the word $MASK$ are arranged in the order as in a dictionary,with or without meaning,which one of the following is the $19^{th}$ word?

$A$ car will hold $2$ persons in the front seat and $1$ person in the rear seat. If among $6$ persons $2$ can drive,then the number of ways in which the car can be filled is

The number of ways in which $5$ girls and $3$ boys can be seated in a row so that no two boys are together is:

In an examination hall,there are $mn$ chairs arranged in $m$ rows and $n$ columns. The number of ways in which $m$ students can be seated such that no row is vacant is:

$10$ men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module