How many automobile license plates can be made if each plate contains two different letters followed by three different digits answer 468000?

The number of automobile license plates that can be made if each plate contains two different letters of English alphabet followed by three distinct digits, is .

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Text Solution

Solution : There are 26 English alphabets and 10 digits (0 to 9). <br> Since, it is given that each plate contains two different letters followed by three different digits. <br> `therefore" "` Arrangement of 26 letters, taken 2 at a time `= ""^(26)P_(2) = (26"!")/(24"!") = 26 xx 25 = 650` <br> and three-digit number can be formed out of the 10 digits `= ""^(10)P_(3) = 10 xx 9 xx 8 = 720` ways <br> `therefore" "` Total number of licence plates `650 xx 720 = 468000`