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

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
Since 2001, the standard serial numbers on a New York state license pl [#permalink]

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30 Dec 2014, 07:38
00:00

Difficulty:

15% (low)

Question Stats:

71% (00:42) correct 29% (00:45) wrong based on 136 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

Kudos for a correct solution.

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Joined: 22 Oct 2014
Posts: 88
Concentration: General Management, Sustainability
GMAT 1: 770 Q50 V45
GPA: 3.8
WE: General Management (Consulting)
Re: Since 2001, the standard serial numbers on a New York state license pl [#permalink]

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30 Dec 2014, 07:57

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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Manager
Joined: 20 Feb 2013
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Location: India
GMAT 1: 690 Q49 V34
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Re: Since 2001, the standard serial numbers on a New York state license pl [#permalink]

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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
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Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: Since 2001, the standard serial numbers on a New York state license pl [#permalink]

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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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Joined: 05 Jun 2018
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Re: Since 2001, the standard serial numbers on a New York state license pl [#permalink]

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30 Jun 2018, 04:52
Would the answer be A if the letters and numbers were not allowed to be repeated
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: Since 2001, the standard serial numbers on a New York state license pl [#permalink]

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30 Jun 2018, 10:32
akshay605 wrote:
Would the answer be A if the letters and numbers were not allowed to be repeated

In this case B would be correct: (26 × 25 × 24) × (10 × 9 × 8 × 7)
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Re: Since 2001, the standard serial numbers on a New York state license pl   [#permalink] 30 Jun 2018, 10:32
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