Question

Serial numbers for a product are to be made using 4 letters followed by 4 digits. the letters are to be taken from the first 9 letters of the alphabet, with no repeats. the digits are to be taken from 0-9 with no repeats. How many serial numbers can be generated?

Answer 1

15,240,960 numbers

Explanation:

To solve this were going to use the principle of permutations. The formula for permutation is given as

P = n! / (n - r)!

Now, the question specifically stated that repeats aren't tolerated, thus for the needed number of serial numbers would be gotten by multiplying the permutation is 4 and 9, by that of the permutation of 4 and 10.

We then have something that is looking like this

Permutation of 4 and 9.

P = 9! / (9 - 4)!

P = 9! / 5!

P = 362,880 / 120

P = 3,024

Permutation of 4 and 10

P = 10! / (10 - 4)!

P = 10! / 6!

P = 3,628,800 / 720

P = 5,040

Multiplying both together would then fetch us our final answer

N = 5,040 * 3,024

N = 15,240,960