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?

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Johnson

Mathematics

15 April, 16:25

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?

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Edith Castro · Answer 1

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