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# If both letters and digits can repeat, which of the following computat

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Joined: 02 Sep 2009
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If both letters and digits can repeat, which of the following computat  [#permalink]

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26 Mar 2018, 00:10
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25% (medium)

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78% (01:13) correct 22% (01:12) wrong based on 47 sessions

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If both letters and digits can repeat, which of the following computations can be used to determine how many different license plate alphanumeric codes consisting of two uppercase letters of the English alphabet followed by four digits are possible?

A. 48

B. 2080

C. 26!/(2!24!)*10!/(4!6!)

D. 26^2*10^4

E. 36^6

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Re: If both letters and digits can repeat, which of the following computat  [#permalink]

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26 Mar 2018, 01:30
Bunuel wrote:
If both letters and digits can repeat, which of the following computations can be used to determine how many different license plate alphanumeric codes consisting of two uppercase letters of the English alphabet followed by four digits are possible?

A. 48

B. 2080

C. 26!/(2!24!)*10!/(4!6!)

D. 26^2*10^4

E. 36^6

Since both letters and digits can repeat, and the 6 digit license plate is formed using
1. Two upper-case letters(of the English Alphabet)
2. Four digits

We know that there are 10 digits(0 - 9) and 26 upper-case characters(A - Z)

Therefore, the various license plate alphanumeric codes possible are $$26^2 * 10^4$$(Option D)
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If both letters and digits can repeat, which of the following computat  [#permalink]

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26 Mar 2018, 16:22
Bunuel wrote:
If both letters and digits can repeat, which of the following computations can be used to determine how many different license plate alphanumeric codes consisting of two uppercase letters of the English alphabet followed by four digits are possible?

A. 48

B. 2080

C. 26!/(2!24!)*10!/(4!6!)

D. 26^2*10^4

E. 36^6

You can use FCP or the "slot method"

26 letters to choose from, repeats allowed
0,1,2,3,4,5,6,7,8,9 = 10 digits, repeats allowed

Six slots ___ ___ ___ ___ ___ ___ ___

First slot, letter = 26 choices
26 * ___ ___ ___ ___ ___

Second slot, letter = 26 choices
26 * 26 * ___ ___ ___ ___

Third slot, numeric digit = 10 choices, which is true for all for remaining slots

26 * 26 * 10 * 10 * 10 * 10
= 26$$^2$$* 10$$^4$$

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Re: If both letters and digits can repeat, which of the following computat  [#permalink]

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27 Mar 2018, 11:36
Bunuel wrote:
If both letters and digits can repeat, which of the following computations can be used to determine how many different license plate alphanumeric codes consisting of two uppercase letters of the English alphabet followed by four digits are possible?

A. 48

B. 2080

C. 26!/(2!24!)*10!/(4!6!)

D. 26^2*10^4

E. 36^6

There are 26 letters in the English alphabet, and there are 10 single digits (0 through 9, inclusive).

Thus, the number of ways to create the license plates is 26 x 26 x 10 x 10 x 10 x 10 = 26^2 x 10^4

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If both letters and digits can repeat, which of the following computat  [#permalink]

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27 Mar 2018, 17:34
_ _ _ _ _ _ = 6 slots to place letter or number
AA1234 = license plate # per question

26 letters can be placed in the first slot, and 26 letters in the 2nd slot. 10 numbers (0 through 9) can go in each of the remaining slots each.

26*26*10*10*10*10 = (26^2) * (10^4)

If both letters and digits can repeat, which of the following computat &nbs [#permalink] 27 Mar 2018, 17:34
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