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HarshaBujji
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A password consists of 6 distinct characters, chosen from the 26 lette 08 Mar 2025, 19:01
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

71% (02:16) correct 29% (02:34) wrong based on 175 sessions

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A password consists of 6 distinct characters, chosen from the 26 letters (A-Z) and 10 digits (0-9). If the first character must be a letter and the last character must be a digit, how many different passwords can be formed?

A) 289,100,800
B) 312,654,720
C) 214,000,000
D) 188,200,000
E) 289,386,240
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E
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A password consists of 6 distinct characters, chosen from the 26 lette 09 Mar 2025, 02:45
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HarshaBujji
A password consists of 6 distinct characters, chosen from the 26 letters (A-Z) and 10 digits (0-9). If the first character must be a letter and the last character must be a digit, how many different passwords can be formed?

A) 289,100,800
B) 312,654,720
C) 214,000,000
D) 188,200,000
E) 289,136,640
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First character is a letter and last character is a digit, let's fill those spaces first: 26 _ _ _ _ 10

The remaining 4 spaces can be filled starting with 25 letter + 9 digits = 34 combined: 26 34 33 32 31 10

Now, just multiplying the last digits of above ignoring 10, we get 4 => last digit will be 0 after multiplying with 10, and second-last digit will be 4.

Only option E. fits.

Answer E.
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stne
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A password consists of 6 distinct characters, chosen from the 26 lette 10 Mar 2025, 08:57
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HarshaBujji
A password consists of 6 distinct characters, chosen from the 26 letters (A-Z) and 10 digits (0-9). If the first character must be a letter and the last character must be a digit, how many different passwords can be formed?

A) 289,100,800
B) 312,654,720
C) 214,000,000
D) 188,200,000
E) 289,136,640
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Please check the OA

\(26*34*33*32*31*10= 289,386,240\)

None of the options fit.
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A password consists of 6 distinct characters, chosen from the 26 lette 10 Mar 2025, 15:19
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HarshaBujji
A password consists of 6 distinct characters, chosen from the 26 letters (A-Z) and 10 digits (0-9). If the first character must be a letter and the last character must be a digit, how many different passwords can be formed?

A) 289,100,800
B) 312,654,720
C) 214,000,000
D) 188,200,000
E) 289,136,640


Please check the OA

\(26*34*33*32*31*10= 289,386,240\)

None of the options fit.
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Edited the OA, thanks!
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A password consists of 6 distinct characters, chosen from the 26 lette 20 May 2026, 08:06
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26* 34* 33*32*31*10 -- used divisibility concept to solve it
Factorising it... (2)^8 , 3, 5, 13, 11, 17, 31
we have one 5 in the number.. so OPTION A,C,D OUT (as they have more than one 5 coz they are multiple of 100)

NOW for B,E - we can check divisibility by 11 and 3

CONCEPT:-
divisibility by 11 requires (SUM of ODD terms - SUM of even terms) -> is either 0 or multiple of 11

OPTION B -312,654,720 = (0+7+5+2+3)-(2+4+6+1) =17-13= 4 (not divisible by 11.. as its not 0 or 11 multiple) so, B OUT
OPTION E -289,386,240 = (0+2+8+9+2)-(4+6+3+8)= 21-21= 0 (we got 0 here.. THUS, divisible by 11)

so, OPTION E imo..
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