# We must create a license plate code that consists of 3 letters followed by 2 digits. Pick a codeat random. What is the chance that the code doesn’t contain any vowel if(a) Repeats are allowed?(b) Repeats are not allowed?

Question
Asked Mar 7, 2020
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We must create a license plate code that consists of 3 letters followed by 2 digits. Pick a code
at random. What is the chance that the code doesn’t contain any vowel if
(a) Repeats are allowed?
(b) Repeats are not allowed?
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Step 1

There are 26 letters and 10 digits.

a)

If repeatation is allowed then we can pick the three letters in (26x26x26)=17576 ways

And we can pick two digits in (10x10)=100 ways.

So total number of number plates= 17576x100=1757600 ways.

Step 2

There are 5 vowels. So there are (26-5)=21 Alphabets

So the letters can be chosen in (21x21x21)=9261

And digits can be chosen in (10x10)=100 ways

So total number ways in which the code doesn’t contain any vowel is = (9261x100)=926100 ways

So the probability that the code doesn&rsq...

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