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Bunuel
How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet)

A. 37×260^2
B. 36×260^2
C. 36×270^2
D. 10^2×26^3
E. 10^3×26^2

Cas1: 2 digits & 3 letters:
_1st_ _2nd_ _3rd_ _4th_ _5th_
1st position can be 0,1,2.......9 (10 possibilities)
Similarly, 2nd position can be 0...9(10 possibilities)
3rd, 4th and 5th each position has 26 possibilities.
Total for Case1 = \(10^2 * 26^3\)
Case2: 3 digits & 2 letters:
_1st_ _2nd_ _3rd_ _4th_ _5th_
1st, 2nd and 3rd each position has 10 possibilities.
4th and 5th each has 26 possibilities.
Total for Case2 = \(10^3 * 26^2\)
Since, it's an or question. Add the possbilities:
\(10^2 * 26^3 + 10^3 * 26^2\)
\(10^2*26^2(26 + 10)\)
\(10^2*26^2*36\)
\(260^2*36\) - (B)
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Hello from the GMAT Club BumpBot!

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