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Since 2001, the standard serial numbers on a New York state license pl

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Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

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New post 30 Dec 2014, 07:38
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A
B
C
D
E

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Question Stats:

72% (00:43) correct 28% (00:49) wrong based on 163 sessions

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Tough and Tricky questions: Combinations.



Since 2001, the standard serial numbers on a New York state license plate are 3 letters followed by 4 digits. How many different license plates are possible if letters and digits can be repeated?

A. 26 × 3 × 10 × 4
B. 26 × 25 × 24 × 10 × 9 × 8 × 7
C. 26³ × 9 × 9 × 9 × 9
D. 26 × 25 × 24 × 10 000
E. 26³ × 10 000

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Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

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New post 30 Dec 2014, 07:57
Answer E.

Since the 7 positions are completely independent from each other, we simply need to multiply the possibilities for each of the 7 positions. Each of the three letters allows 26 combinations (assuming 26 different letters) and the digits allow 10 different combinations for each position. We therefore get:

\(26 * 26 * 26 * 10 * 10 * 10 * 10 = 26^3 * 10 ^4 = 26 ^3 * 10,000\)
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Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

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New post 30 Dec 2014, 22:25
Solution:
3 repeated letters can be chosen as 26 * 26 * 26
4 repeated digits can be chosen as 10 * 10 * 10 * 10
Answer E
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Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

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New post 08 Jan 2015, 08:18
Bunuel wrote:

Tough and Tricky questions: Combinations.



Since 2001, the standard serial numbers on a New York state license plate are 3 letters followed by 4 digits. How many different license plates are possible if letters and digits can be repeated?

A. 26 × 3 × 10 × 4
B. 26 × 25 × 24 × 10 × 9 × 8 × 7
C. 26³ × 9 × 9 × 9 × 9
D. 26 × 25 × 24 × 10 000
E. 26³ × 10 000

Kudos for a correct solution.


OFFICIAL SOLUTION:

(E) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 × 10 for the four digits. The number of different license plates is 26 × 26 × 26 × 10 × 10 × 10 × 10 = 26³ × 10 000.

The correct answer is choice (E).
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

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New post 30 Jun 2018, 04:52
Would the answer be A if the letters and numbers were not allowed to be repeated
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Re: Since 2001, the standard serial numbers on a New York state license pl  [#permalink]

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New post 30 Jun 2018, 10:32
Re: Since 2001, the standard serial numbers on a New York state license pl &nbs [#permalink] 30 Jun 2018, 10:32
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