Serial numbers for a product are to be made using 2 letters followed by 2 digits. The letters are to be taken from the first 6 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?

Alright so I'm coming up with this on the fly; you have the first six letters (a, b, c, d, e, f) and 0-9 and your ten numbers. calculate the amount of possible combinations for the letters by simply writing them down.

ab, ac, ad, ae, a f - five

bc, bd, be, bf - four

cd, ce, cf - three

de, df - two

ef, - one.

adding these all together gets a total of 15 for the letters. now the numbers

01, 02, 03, 04, 05, 06, 07, 08, 09 - nine

12, 13, 14, 15, 16, 17, 18, 19 - eight

23, 24, 25, 26, 27, 28, 29 - seven

34, 35, 36, 37, 38, 39 - six

45, 46, 47, 48, 49 - five

56, 57, 58, 59 - four

67, 68, 69 - three

78, 79 - two

89 - one

added together with a total of 45 combinations.

alright so, 45 different number combinations and 15 letter combinations. multiplying 15 by 45 should tell you the total possible combinations for a two letter and two number serial-number