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gracygupta23
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A certain stock exchange designates each stock with a one-, two- or th 31 Aug 2025, 08:12
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Shouldn't we divide the two-digit code by 2 factorial and similarly three digit code by 3 factorial to eliminate repetition of the same letters like AAA or BBB etc? Even though repetition is allowed, we can't possibly shift these letters to make a new code.
Bunuel
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 a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

A. 2951
B. 8125
C. 15600
D. 16302
E. 18278

1 letter codes = 26
2 letter codes = 26^2
3 letter codes = 26^3

Total = 26 + 26^2 + 26^3

The problem we are faced now is how to get the answer quickly. Note that the units digit of 26+26^2+26^3 would be (6+6+6=18) 8. Only one answer choice has 8 as unit digit: E (18,278). So I believe, even not calculating 26+26^2+26^3, that answer is E.
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A certain stock exchange designates each stock with a one-, two- or th 31 Aug 2025, 08:41
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gracygupta23
Shouldn't we divide the two-digit code by 2 factorial and similarly three digit code by 3 factorial to eliminate repetition of the same letters like AAA or BBB etc? Even though repetition is allowed, we can't possibly shift these letters to make a new code.

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3 or 2 similar letters won't repeat; take a small example of 2 letters A and B => we get 2*2 = 4 different arrangements, viz. AA, AB, BA, BB. Similarly for 26 letters, you would get different no. of arrangements, you won't need to divide.
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A certain stock exchange designates each stock with a one-, two- or th 22 Jul 2026, 08:12
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A = 26C1
AB = 26C2*2!
AA = 26C1*1C1
AAA = 26
AAB = 26C1*1C1*25C1 *3!/2!
ABC = 26C3*3!

total = 18278 E
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A certain stock exchange designates each stock with a one-, two- or th 27 Jul 2026, 12:33
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Hi Bunuel, can you tell me why it's not (26)^2/2! are the letters not identical in some cases like AA, BB and so on? I am little bit confused in this

Thanks :-)
Bunuel
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 a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

A. 2951
B. 8125
C. 15600
D. 16302
E. 18278

1 letter codes = 26
2 letter codes = 26^2
3 letter codes = 26^3

Total = 26 + 26^2 + 26^3

The problem we are faced now is how to get the answer quickly. Note that the units digit of 26+26^2+26^3 would be (6+6+6=18) 8. Only one answer choice has 8 as unit digit: E (18,278). So I believe, even not calculating 26+26^2+26^3, that answer is E.
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A certain stock exchange designates each stock with a one-, two- or th 27 Jul 2026, 12:41
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Rhitib
Hi Bunuel, can you tell me why it's not (26)^2/2! are the letters not identical in some cases like AA, BB and so on? I am little bit confused in this

Thanks :-)

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We do not divide by 2! because the order of the letters matters: AB and BA are different codes.

Also, identical-letter codes such as AA are counted only once in 26^2, so there is no overcounting to correct.
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