How many numbers greater than 1000000 can be | vedclass

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

Question

(A) The given digits are $0, 1, 2, 2, 2, 4, 4$. There are $7$ digits in total.Since $1000000$ is a $7$-digit number,any $7$-digit number formed using

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(A) The given digits are $0, 1, 2, 2, 2, 4, 4$. There are $7$ digits in total.Since $1000000$ is a $7$-digit number,any $7$-digit number formed using these digits will be greater than $1000000$ as long as it does not start with $0$.Total permutations of these $7$ digits (treating $0$ as a digit) is $\frac{7!}{3!2!} = \frac{5040}{6 	imes 2} = 420$.However,we must exclude numbers starting with $0$. If $0$ is fixed at the first position,the remaining $6$ digits are $1, 2, 2, 2, 4, 4$.The number of such arrangements is $\frac{6!}{3!2!} = \frac{720}{6 	imes 2} = 60$.Therefore,the number of $7$-digit numbers greater than $1000000$ is $420 - 60 = 360$.

How many numbers greater than $1000000$ can be formed by using the digits $1, 2, 0, 2, 4, 2, 4$?

Similar Questions

The number of ways in which the following prizes can be given to a class of $20$ boys,first and second Mathematics,first and second Physics,first Chemistry,and first English is:

Ten 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:

How many numbers can be formed using the digits $3, 4, 5, 6, 7, 8$ that lie between $3000$ and $4000$ and are divisible by $5$,given that repetition of digits is not allowed?

How many $8$-digit numbers can be formed such that all digits are distinct?

If $4 \times ^{15}P_r = 3 \times ^{16}P_{r-1}$,then $r = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module