Question

A series if license plates are being produced that all have the same pattern of three letters (a-z) followed by three digits (0-9) without any repeats. If no letters or numbers are repeated, how many different possibilities are there? what is the probability that the license plate is ABC123 or MOM678?

Answer 1

If no letters or numbers are repeated, then the number of possibilities will be 11,232,000. Then the probability that the license plate is ABC123 or MOM678 will be 1/8,788,000.

What are permutation and combination?

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

A series of license plates are being produced that all have the same pattern of three letters (a-z) followed by three digits (0-9) without any repeats.

If no letters or numbers are repeated, then the number of the possibilities will be

Number of ways = 26 × 25 × 24 × 10 × 9 × 8

Number of ways = 11,232,000

Then the probability that the license plate is ABC123 or MOM678 will be

$P = \dfrac{1}{17,576,000}+\dfrac{1}{17,576,000}\\\\P = \dfrac{1}{8,788,000}$

More about the permutation and the combination link is given below.

brainly.com/question/11732255

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