type the correct answer in the box. a standard new york car license plate has 3 letters followed by 4…

type the correct answer in the box. a standard new york car license plate has 3 letters followed by 4 numbers. if the letters and numbers can be repeated, the number of distinct license plates that can be created in the given pattern is

type the correct answer in the box. a standard new york car license plate has 3 letters followed by 4 numbers. if the letters and numbers can be repeated, the number of distinct license plates that can be created in the given pattern is

Answer

Explanation:

Step1: Calculate letter - combination possibilities

There are 26 letters in the alphabet and 3 letter - positions with repetition allowed. So the number of letter - combination possibilities is $26\times26\times26 = 26^{3}$.

Step2: Calculate number - combination possibilities

There are 10 digits from 0 - 9 and 4 number - positions with repetition allowed. So the number of number - combination possibilities is $10\times10\times10\times10=10^{4}$.

Step3: Calculate total license - plate possibilities

By the multiplication principle, the total number of distinct license plates is the product of the number of letter - combination possibilities and number - combination possibilities. So it is $26^{3}\times10^{4}$. $26^{3}=26\times26\times26 = 17576$, and $17576\times10^{4}=175760000$.

Answer:

175760000