A 4-digit code is to be formed from the digits $0,1,2,3,4,5,6,7,8$ and 9 . No digit may be used more than once in any code. A code may start with 0 . (ii) Find how many codes form an odd number.
Explanation
For a number to be odd, the units digit must be odd. There are 5 odd digits (1, 3, 5, 7, 9) out of 10 digits. The first digit can be any of the 10 digits, the second digit can be any of the remaining 9 digits, the third digit can be any of the remaining 8 digits, and the fourth digit can be any of the remaining 5 odd digits. So, the total number of codes that form an odd number is 10 * 9 * 8 * 5 = 3600.
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