AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order. From how many different passwords can Will choose?
A. 390
B. 2,340
C. 4,680
D. 7,020
E. 14,040
Here's another approach.
There are three possible cases that satisfy the given information.
case i: The password is in the form letter-digit-digit
case ii: The password is in the form digit-letter-digit
case iii: The password is in the form digit-digit-letter
case i: The password is in the form letter-digit-digitThere are 26 ways to select the only letter
There are 10 way to select the first digit
There are 9 ways to select the other digit (it can be any digit except the digit we chose for second position)
So the total number of passwords in the form letter-digit-digit = (26)(10)(9) =
2340case ii: The password is in the form digit-letter-digitThere are 10 ways to select the first digit (0,1,2,3,4,5,6,7,8 or 9)
There are 26 ways to select the only letter
There are 9 way to select the other digit (it can be any digit except the digit we chose for first position)
So, the total number of passwords in the form digit-letter-digit = (10)(26)(9) =
2340As you might guess, the third case can also be accomplished in
2340 ways
Answer: (3)(
2340) = 7020
Answer: D
Cheers,
Brent
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Brent Hanneson – Creator of gmatprepnow.com
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