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# Is this question is a combination or a permutations? and how to solve it step by step ?

How many licence plates of three symbols (letters and digits) can be made using at least one letter in each?

### 2 Answers by Expert Tutors

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
4.9 4.9 (21 lesson ratings) (21)
2
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

@Arthur D. Thank you very much
You're very welcome, Amin.
Paul M. | Learn "how to" do the math and why the "how to" works!Learn "how to" do the math and why the "...
5.0 5.0 (1 lesson ratings) (1)
2
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!