ratnanideepak wrote:
there are 6 distinct letters of the English alphabet and 4 distinct digits. all possible 6 character apha-numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?
A. 4320
B. 64800
C. 8800
D. 22000
Dear
ratnanideepakI'm happy to respond.
There seems to be a couple problems here. First of all, there are only four answer choices, whereas all GMAT Quant questions have five choices. On the real GMAT, and on all better prep sources, numerical answers always appear in numerical order, at least for positive integers.
From the six letters, we need four distinct letters
# of combinations = 6C4 = 15
From the four numerals, we need 2 distinct digits
4C2 = 6
Once we have our unique four letter and our unique 2 digits, we can put them in any order: each new order would be a different code. The number of orders would be
6! = 720
Now, we use the
Fundamental Counting Principle. See:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/Total number of codes equals = 15*6*720
Without a calculator, first do 15*6 = 90. Then, 90 = 100 - 10, so
720*90 = 720*(100 - 10) = 72000 - 7200 =
64800Answer =
(B) Does all this make sense?
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)