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

#### Solution

Numbers greater than a million can be formed when the first digit can be any one out of the given digits 1, 2, 0, 2, 4, 2, 4, except 0.

Number of arrangements of the given digits 1, 2, 0, 2, 4, 2, 4 = Arrangements of 7 things of which 3 are similar to the first kind, and 2 are similar to the second kind =\[\frac{7!}{2!3!}\]

But, these arrangements also include the numbers in which the first digit is zero. This will make the number less than a million. So, it needs to be subtracted.

Number where the first digit is zero = Number of arrangements of the remaining 6 digits 1, 2, 2, 4, 2, 4 =\[\frac{6!}{2!3!}\]

Numbers greater than 1 million =\[\frac{7!}{2!3!}\]-\[\frac{6!}{2!3!}\]= 360