How many 4-digit numbers can you form with (1,2,3,4,5,6,7) ?
(No repeated numbers)
The answer is: .
But how many of these are odd numbers?
The last (rightmost) digit must be odd; there are choices: 1, 3, 5, or 7.
The other three digits are chosen from the remaining six digits: . ways.
Therefore, there are: . odd numbers.