Suppose The DMV is issuing car license plates that consistin

Suppose The DMV is issuing car license plates that consisting of the three letters followed by four digits. How many possible license plates can be issued. How many possible plates with the three letters are \"KTU\" followed by any four digits. What is the probability of having one of these \"KTU\" plates.

Solution

3 letters followed by 4 digits

NOrmally in car licence plates repitition of numbers or alphabets are allowed

If repitition not allowed, then there are 26 alphabets and 10 digits from 0,1,2,3,4.....9

I letter can be selected in 26 ways and second from remaining 25 letters in 25 ways and iii from remaining 24 in 24 ways,....

Similarly numbers I number any one of the 10, ii any one of the remaining 9, etc.

Hence no of ways = no of ways of selecting 3 letters from 26 letters * No of ways of selecting 4 digits from 10 numbers

= (26)(25)(24)(10)(9)(8)(7)

=78624000.

If repitition is allowed no of ways = 26^4 (10^4)

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When three letters are decided as KTU.

There is only one way for selecting alphabets as that is fixed KTU.

Only numbers we have choices. I number can be selected from 10 numbers in 10 ways, II in 9 ways, ....

then 4 numbers can be selected in 10(9)(8)(7)

= 5040

If repitition is allowed, 10^4 = 10000 ways

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NOte : If repitition is allowed then each alphabet can be selected from 26 and hence no of ways

= 26