find the number of seven-digit numbers which can be formed with the sum of the digits being odd.
my approach is breaking down all the cases :
Case 1 : first digit is odd --> 5waysEg: 1000000 etc
Case 2: Odd + even : 5c1 * 4c1 *2 = 40 way Eg :1200000 , 1400000Case 3 : One odd + Even repeated twice : 5c1 * 4c1 *3 = 60 Eg:1220000 , 221000 eg ..
Case 4 : One odd + Even repeated thrice : 5c1 * 4c1 *4= 80 Eg:1222000 , 221200 eg ..
But this way will take time . Please give shortcut