numbers greater than a million can be formed with the digits 2,3,0,3,4,2,3 .

Step-by-step solution

All seven-digit numbers formed with the given digits are greater than a million. Note that the digit at millions place cannot be 0 . It can be any one of the digits 2,3,4 . Case I : Digit at millions place is ' 2 '. Remaining 6 digits can be arranged in 6! 3! =120 ways. Case II : Digit at millions place is ' 3 '. Remaining 6 digits can be arranged in 6! 2! 2! =180 ways. Case III : Digit at millions place is ' 4 '. Remaining 6 digits can be arraigned in 6! 3! 2! =60 ways aligned Required number of numbers & =120+180