EgmatQuantExpert wrote:
A 3-character alpha-numeric code does have the following properties – the first character can be any number except 0 and 9, the second character can be any small letter between a to z, excluded, and the third character can have any of those characters possible for the first two places. How many such codes can be formed?
A. 26
B. 64
C. 520
D. 6144
E. 9360
The 3 character alpha-numeric code has the following characters
First character - Any number except 0 and 9 - Total of 10 - 2 = 8 possibilities
Second character - Any small letter except a and z - Total of 26 - 2 = 24 possibilities
Third character - Any number except 0 and 9 or Any small letter except a and z - Total of 8 + 24 = 32 possibilities
In this case, to find the total number of possibilities, we can use the unit's digit to find the
answer as number ending 8 * number ending 4 * number ending 2 is a number ending 4.
Also, the answer must be close to 10*20*30 is a little more than 6000.
P.S when the answer options are far apart, we can use approximations to arrive at the answerTherefore,
Option D(6144) is the the total number of 3-character alpha-numberic codes.
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