Asked by Anonymous

What is the probability of getting a license plate that has a repeated letter or digit if you live in a state that has four letters followed by two numerals followed by two letters? (Round to the nearest whole percent.)

Answers

Answered by Reiny
number of total plates including all possible repetitions
= 26^4*100*26^2 = 30 891 577 600 (wow, enough until cars become "extinct")

so what we don't want are cases where all letters and numbers are different, which would be
26*25*24*10*9*23*22 = 710 424 000

so prob with some kind of repeats
= 1 - .710 424 000/30 891 577 600
= appr .9777 or 98% to the nearest percent
Answered by MathMate
The licence plate template is
XXXXNNXX
with 6 letters and two numbers.

The number of licence plates without repetition, i.e. without choosing a previously used character or number is
=26.25.24.23.10.9.22.21
=C(26,6)*C(10,2)
The number of licence plates without regard to repetition is
=26^6*10*2

The probability P1 of getting a licence plate with<b>out</b> repetition is the first divided by the second.

The probability of getting a plate <b>with</b> repetition is 1-P1.
Answered by MathMate
Sorry,
26.25.24.23.10.9.22.21
is <i>not</i> C(26,6)*C(10,2)
The rest of the calculations should be good.
Answered by Reiny
looks like this is the day for errors

I left out one of the letters in the first group of letters

should have said:

<b>so what we don't want are cases where all letters and numbers are different, which would be
26*25*24*23*10*9*22*21 = 14 918 904 000</b>

so the prob as asked in your question
= 1 - 14 918 904 000/30 891 577 600
= .517
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