Inactive Tutor answered 06/01/15
Ariana G.
asked 05/31/15I need help with this difficult word problem
Before the 1976, California license-plate numbers consisted of three numbers (for example, EGT 893). In the summer of 1976, however, the state ran out of numbers of this type and started issuing seven-digit plates (such as GIR 788 1). How many possible license plate numbers can be made from 3 letters followed by 4 numerical digits? (Base your answer on 26 letters in the alphabet and 10 numerical digits.)
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2 Answers By Expert Tutors
Tutor
New to Wyzant
There may be 3 letters (A-Z) with 4 numbers (0-9), so
26*26*26*10*10*10*10 = 175760000 possibilities
Inactive Tutor answered 05/31/15
Tutor
New to Wyzant
Since repetition is allowed and order does make a difference, the number of plates is:
26 · 26 · 26 · 10 · 10 · 10 · 10 = 4569760000
Inactive Tutor
Too many 26's in that number! How about 175,760,000 ?
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05/31/15
Inactive Tutor
How do you come to the conclusion that there is one too many 26's?
The problem says "3 letters." For each letter there are 26 possibilities.
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05/31/15
Inactive Tutor
By multiplying:
26*26*26*26*10*10*10*10 = 4569760000 (with one too many 26's)
and 26*26*26*10*10*10*10 = 175760000 (the answer)
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06/01/15
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Inactive Tutor
05/31/15