Question

How many numbers greaters than a million can be formed by using the digits 4,6,0,6,8,4,6?

Answer 1

Consider given the number $4,6,0,6,8,4,6$.

Here one million $=10,00,000$. Given numbers are 4,6,0,6,8,4,6.

A number greater than $1000000$ has $7$ places, and all the digits are to be used. But $4$ is repeated twice and $6$ is repeated thrice.
The total number of ways arranging $7$ digits when 4 and 6 are repeated $=\frac{7!}{2!3!}=420$.
But the numbers that begin with $0$ are no more seven-digit numbers then reject those numbers.
Therefore, by not including Zero and taking the six digits number formed. These can be arranged as follow: $\frac{6!}{2!3!}=60$
∴ required number of arrangements $=420-60=360$

Hence, this is the answer.