PERMUTATION FOR SERIAL NUMBERS

Question

Serial numbers for a product are to be made using 4 letters followed by 3 digits. The letters are to be taken from the first 9 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

For 4 letters choosing 4 from 9 (a,b,c,d,e,f,g,h,i)/

Since there are no repeats, one way to calculate is:

9(8)(7)(6).--9 choices for 1st spot, then 8 for 2nd, and so on.

This is really the permutation of 9 "things" taken 4 at a time.

For 3 digits:

10(9)(8)

The final answer is :

9(8)(7)(6)(10)(9)(8)

This is an application of the fundamental counting principle.

Check it out here:

desmos.com/calculator/nhjz8sahrr