how many numbers greater than 1000000 can be formed by using the digits 1,2,0,2,4,2,4?
Since, 1000000 is a 7-digit number and the number of digits to be used is also
7. Therefore, the numbers to be counted will be 7-digit only. Also, the numbers have to
be greater than 1000000, so they can begin either with 1, 2 or 4.
The number of numbers beginning with 1 =
6! 4 5 6
3! 2! 2
× ×
= = 60, as when 1 is
fixed at the extreme left position, the remaining digits to be rearranged will be 0, 2, 2, 2,
4, 4, in which there are 3, 2s and 2, 4s.
Total numbers begining with 2
= 6! 3 4 5 6
2! 2! 2
× × ×
= = 180
and total numbers begining with 4
6! 4 5 6
3!
= = × × = 120