A certain stock exchange designates each stock with a one, two, or three letter code where each letter is selected from the 26 letters of the alphabet. if the letters may be repeated and if the same letters used in different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes
a) 2951 b) 8,125 c) 15,600 d) 16,302 e) 18,278
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teejaycrown
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Anurag@Gurome
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Number of possible one-letter codes = 26teejaycrown wrote:A certain stock exchange designates each stock with a one, two, or three letter code where each letter is selected from the 26 letters of the alphabet. if the letters may be repeated and if the same letters used in different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes
a) 2951 b) 8,125 c) 15,600 d) 16,302 e) 18,278
Number of possible two-letter codes = 26*26
Number of possible three-letter codes = 26*26*26
Hence, total number of possible codes = 26 + 26*26 + 26*26*26
No need to calculate the above. Just notice that unit's digit of all the underlined term ends with 6. Hence, unit's digit of the correct answer will be unit's digit of (6 + 6 + 6) = unit's digit of 18 = 8.
Only option E has 8 as unit's digit.
Hence, the correct answer is E.
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Case 1: one-letter codesteejaycrown wrote:A certain stock exchange designates each stock with a one, two, or three letter code where each letter is selected from the 26 letters of the alphabet. if the letters may be repeated and if the same letters used in different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes
a) 2951 b) 8,125 c) 15,600 d) 16,302 e) 18,278
Number of options for the one letter = 26.
Case 2: two-letter codes
Number options for the first letter = 26.
Number of options for the second letter = 26.
To combine these options, we multiply:
26*26.
Case 3: three-letter codes
Number options for the first letter = 26.
Number of options for the second letter = 26.
Number of options for the third letter = 26.
To combine these options, we multiply:
26*26*26.
Total possible codes = Case 1 + Case 2 + Case 3 = 26 + 26*26 + 26*26*26.
Since each of the three terms will have a units digit of 6, and 6+6+6 = 18, the units digit of the correct answer must be 8.
The correct answer is E.
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As a tutor, I don't simply teach you how I would approach problems.
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