Question

Serial numbers for a product are to be made using 3 letters followed by 3 digits. The letters are to be taken from the first 5 letters of the alphabet, with no repeats. The digits are taken from the 10 digits 0,1,2,... , 9 with no repeats. How many serial numbers can be generated

Answer 1

43,200 serial numbers can be generated

Explanation:

The ordering for the letters and the digits are important. For example, 012 constitutes a different serial number than 210. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

How many serial numbers can be generated

3 letters, from the first five of the alphabet

3 digits, from a set of 10

So

`T = P_(5,3)*P_(10,3) = (5!)/((5-3)!)*(10!)/((10-3)!) = 43200`

43,200 serial numbers can be generated