To calculate: The number of different license plates that can be formed if a license plate begin with two letters followed by four digits or begin with three digits followed by three letters. Assume that no letters or digits are repeated.
The resultant license plates are
Given information:
Every license plate begins with two letters, followed by four letters or begins with three digits followed by three letters.
Formula used: The number of permutations of n objects taken r at a time denoted by
Calculation:
There are 26 letters and 10 digits from 0 to 9.
There are 2 cases, First case says “The first two places are filled with 2 letters and remaining places are filled with 4 digits.”
The first two places can be filled by
The expression can be written as:
Rewrite the expression using the formula
Now expand the factorial,
Therefore, the number of license plates in which first two places are filled with 2 letters and remaining places are filled with 4 digits is
Now consider the second case, “The first three places are filled with 3 digits and remaining places are filled with 3 letters.”
The first three places can be filled by
The expression can be written as:
Rewrite the expression using the formula
Now expand the factorial,
Therefore, the number of license plates on second case is
The total number of possible license plates from both cases will become:
Therefore, the number of possible license plates is 14,508,000.
Chapter 9 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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