Question

Ali and Mel are making 3-digit codes.

The digit 0 is not used.
Ali only uses odd digits.
Mel only uses even digits.

Ali can make x more codes than Mel.
Assume that digits cannot be repeated.
Work out the value of x.

Answer 1

x = 36

Explanation:

You want to know how many more 3-digit codes can be made from odd numbers than from even numbers if 0 is excluded and no digit can be repeated.

Code count

The number of possible codes will be the product of the number of available digits for each position in the code.

There are 5 odd digits, so Ali has 5 available digits for the first position, 4 for the next, and 3 for the last. (Using a digit makes it unavailable for a different position.) Ali can make 5·4·3 = 60 codes

There are 4 even digits when 0 is excluded, so Mel has 4 available digits for the first position, 3 for the next, and 2 for the last. Mel can make 4·3·2 = 24 codes.

Difference

Ali can make x more codes than Mel, where ...

x = 60 -24 = 36