Arthur D. answered • 07/26/18

Forty Year Educator: Classroom, Summer School, Substitute, Tutor

Arthur D.

07/27/18

Amin X.

asked • 07/26/18How many licence plates of three symbols (letters and digits) can be made using at least one letter in each?

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Arthur D. answered • 07/26/18

Tutor

4.9
(88)
Forty Year Educator: Classroom, Summer School, Substitute, Tutor

you don't say if you can have repetitions or not

I'll assume no repetitions; if there are repetitions you can make the changes.

it is a permutation problem

at least one letter means you could have 1 letter, 2 letters or 3 letters

case 1: 1 letter

L=letter and N=number

LNN, NLN, or NNL

26 letters and 10 digits

26*10*9+10*26*9+10*9*26=7020

notice all 3 numbers are the same each time so you could multiply one product by 3 also

case 2: 2 letters

LLN, LNL, or NLL

26*25*10+26*10*25+10*26*25=19,500

case 3: 3 letters

26*25*24=15,600

add 15,600+19,500+7020=42,120

Arthur D.

tutor

You're very welcome, Amin.

Report

07/27/18

You need to specify whether repeats are allowed.

You can select the place for the required letter in 3 ways and fill it in 26 ways.

If repeats are allowed then there are 3*26*36*36 license plates.

If repeats are not allowed then 3*26*35*34 plates.

In either event a BIG number of plates!

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Amin X.

07/27/18