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The transportation department predicts that about 800,000 cars will be registered in a certain state by year 2012. Their license plates are made using and two letters followed by and three digits from 0 to 9. Will there be enough possible arrangements?

Respuesta :

MrRoyal

Answer:

There won't be enough arrangement

Step-by-step explanation:

Given

[tex]Letters = 2[/tex]

[tex]Digits= 3[/tex]

[tex]Cars = 800000[/tex]

Required

Determine if the possible arrangement will be enough

The 2 letters can be selected from any of the 26 alphabets without restriction.

So, the selection of letters is:

[tex]Letters = 26 * 26[/tex]

The 3 digits can be selected from any of the 10 digits without restriction.

So, the selection of digits is:

[tex]Digits = 10*10*10[/tex]

The total arrangement is:

[tex]Total = Letters * Digits[/tex]

[tex]Total = 26*26*10*10*10[/tex]

[tex]Total = 676000[/tex]

By comparison:

[tex]Total < Cars[/tex]

i.e.

[tex]676000 < 800000[/tex]

Hence, the arrangement will not be enough

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