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A small nation issues license plates that consist of just one number

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A small nation issues license plates that consist of just one number  [#permalink]

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New post 03 Jan 2019, 09:10
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Question Stats:

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A small nation issues license plates that consist of just one number (selected from the digits 0 through 9, inclusive) and four letters, selected from a 20-letter alphabet. Repeats are permitted. However, there is one four-letter combination that is not allowed to appear on license plates. How many allowable license plate combinations exist?


(A) 1,599,990
(B) 1,599,999
(C) 1,600,000
(D) 4,569,759
(E) 4,569,760

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Re: A small nation issues license plates that consist of just one number  [#permalink]

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New post 03 Jan 2019, 22:05
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A small nation issues license plates that consist of just one number (selected from the digits 0 through 9, inclusive) and four letters, selected from a 20-letter alphabet. Repeats are permitted. However, there is one four-letter combination that is not allowed to appear on license plates. How many allowable license plate combinations exist?

Total slots = 5 [ digit, letter, letter, letter, letter ]

slot 1 : 10 possibilities (0-9)
slot 2 : 20 possibilities (20 letters)
slot 3: 20 possibilities (20 letters : repetition allowed)
slot 4: 20 possibilities
slot 5 : 20 possibilities

total ways= 10* (20)^4

disallowed combinations: 10*1

answer : 10*(20)^4 - 10
10* [ (20)^4 -1 ]
10*159999 = 1599990

A
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Re: A small nation issues license plates that consist of just one number  [#permalink]

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New post 03 Jan 2019, 22:08
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kanakdaga wrote:
A small nation issues license plates that consist of just one number (selected from the digits 0 through 9, inclusive) and four letters, selected from a 20-letter alphabet. Repeats are permitted. However, there is one four-letter combination that is not allowed to appear on license plates. How many allowable license plate combinations exist?

Total slots = 5 [ digit, letter, letter, letter, letter ]

slot 1 : 10 possibilities (0-9)
slot 2 : 20 possibilities (20 letters)
slot 3: 20 possibilities (20 letters : repetition allowed)
slot 4: 20 possibilities
slot 5 : 20 possibilities

total ways= 10* (20)^4

disallowed combinations: 10*1

answer : 10*(20)^4 - 10
10* [ (20)^4 -1 ]
10*159999 = 1599990

A


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Re: A small nation issues license plates that consist of just one number  [#permalink]

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New post 06 Jan 2019, 05:46
Bunuel wrote:
A small nation issues license plates that consist of just one number (selected from the digits 0 through 9, inclusive) and four letters, selected from a 20-letter alphabet. Repeats are permitted. However, there is one four-letter combination that is not allowed to appear on license plates. How many allowable license plate combinations exist?


(A) 1,599,990
(B) 1,599,999
(C) 1,600,000
(D) 4,569,759
(E) 4,569,760


1 no would be 10
and 4 letters 20^4
so total 10*20^4 = 16*10^5
one combination of 4 letter not allowed to appear on license plates = 1^4 * 10 = 10

so left with valid no= 16*10^5-10 = 159990 IMO A
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Re: A small nation issues license plates that consist of just one number  [#permalink]

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New post 11 Jan 2019, 05:27
Bunuel wrote:
A small nation issues license plates that consist of just one number (selected from the digits 0 through 9, inclusive) and four letters, selected from a 20-letter alphabet. Repeats are permitted. However, there is one four-letter combination that is not allowed to appear on license plates. How many allowable license plate combinations exist?


(A) 1,599,990
(B) 1,599,999
(C) 1,600,000
(D) 4,569,759
(E) 4,569,760

I was confused with the wording one four letter combination is not allowed
Lets say it was
FUKC
Did they mean
FKUC and other combinations not allowed too.
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Re: A small nation issues license plates that consist of just one number  [#permalink]

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New post 20 Jan 2019, 15:17
I think the question stem needs to be a bit clearer. It does not specify that the numerical digit can only appear in one position!
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Re: A small nation issues license plates that consist of just one number  [#permalink]

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New post 29 Jan 2019, 14:01
KomalSg wrote:
Bunuel wrote:
A small nation issues license plates that consist of just one number (selected from the digits 0 through 9, inclusive) and four letters, selected from a 20-letter alphabet. Repeats are permitted. However, there is one four-letter combination that is not allowed to appear on license plates. How many allowable license plate combinations exist?


(A) 1,599,990
(B) 1,599,999
(C) 1,600,000
(D) 4,569,759
(E) 4,569,760

I was confused with the wording one four letter combination is not allowed
Lets say it was
FUKC
Did they mean
FKUC and other combinations not allowed too.



The combination remains same, in your case "FKUC" however this is to be suffixed with a digit and that digit can be any between 0 to 9. Hence. 10 options to be subtracted.
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Re: A small nation issues license plates that consist of just one number   [#permalink] 29 Jan 2019, 14:01
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