Serial numbers for a product are to be made using 2 letters followed by 3 numbers. If the letters are to be taken from the first 6 letters of the alphabet with no repeats and the numbers are taken from the digits 0 through 9 with repeats possible, how many serial numbers can be generated?

2 Letters chosen among 6 with no repeat:

a) the first has 6 ways

the second has 5 ways

Then to choose 2 letters among 6, with no repeat, there are 6x5 = 30 ways

b) 3 numbers are taken from the digits 0 through 9 with repeats (total = 10)

the first has 10 ways

the second has 10 ways

the third has 10 ways

Then to choose 3 numbers among 10, with repeat, there are 10x10x10 = 1000 ways

And the total serial numbers that can be generated is

30 x 1000 = 3000