Question

How many different 4-digit numbers can be made from the set of 8 numbers {1, 2, 3, 4, 5, 6, 7, 8} if: The resulting number must be an odd number and repeats are NOT allowed.

Answer 1

If the number is an odd number, at unit place, it must have 1 or 3 or 5 or 7, i.e. 4 ways. For rest of 3 places, we have 7 choices. Since repetition is not allowed so the no that has been placed at unit place can't be used at other places. So the remaining 3 places can be filled in

P(7,3) = 210 ways.

So total no of ways = 4•210 = 840 ways