How many numbers greater than 1000000 can be | vedclass

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(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 $1, 2, 0, 2, 4, 2, 4$?

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