1. ## number of possibilities

how many 4 digit numbers can you form with (1,2,3,4,5,6,7) ? (No repeated numbers)

BUT

How many of these are odd numbers?

I know that there are 4 odd numbers...

2. Hello, Faisal2007!

How many 4-digit numbers can you form with (1,2,3,4,5,6,7) ?
(No repeated numbers)

The answer is: . $_7P_4 = 840$

But how many of these are odd numbers?

The last (rightmost) digit must be odd; there are ${\color{blue}4}$ choices: 1, 3, 5, or 7.

The other three digits are chosen from the remaining six digits: . $_6P_3 = {\color{blue}120}$ ways.

Therefore, there are: . $4\cdot120 \:=\:480$ odd numbers.

3. Why is it 4 * 120 ?