How many 5 digit zipcodes 09 are possible if the first digit

How many 5 digit zipcodes (0-9) are possible if the first digit must be odd, the next two must be even (don\'t count 0), and the last two can be any remaining digit. (No digits can repeat.) A: 2520

Solution

There are 5 places.

First place can be filled up by 5 odd digits (1/3/5/7/9)

The second place can be filled up by 4 even digits(2/4/6/8)

Then third place can be filled up by rest 3 even digits.

Fourth place can be filled up by remaining 7 digits.

Fifth  place can be filled up by remaining 6 digits.

so total number of way = 5 x 4 x 3 x 7 x 6 = 2520