Question

The total number of numbers of distinct 4 digit odd numbers if the digit used is not repeated again is

• A. 2240
• B. 2220
• C. 2780
• D. 2000

Answer 1

The correct option is A 2240

Let the number be abcd, where a,b,c and d are the digits.
The digit d can take 5 values. (1,3,5,7 and 9).

The digit 'a' can take any digit from 1 to 9 (it cannot take zero because it won't be a 4 digit number then). However, the value of a cannot be the same as that of d. Thus, we can have 8 possible values for the digit 'a'.
The digit b can be 0 as well. However, it cannot be the same as a or d. Hence, we can have 8 possible values for the digit 'b'.

Similarly, we can have 7 possible values for the digit 'c'

Thus, the number of four digit numbers which satisfy the above condition = $8\times 8\times 7\times 5=2240$