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?  Choose the correct option:
A) 4320
B) 64800
C) 8800
D) 22000
E) 6600
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   Total number of codes equals =  15*6= 
<gadget id="calculator"> 15*6</gadget>
<output>90</output>
90. Then, 90= 100 - 10, so   720*90 = 720*(100 - 10) = 72000 - 7200= 
<gadget id="calculator">72000 - 7200</gadget>
<output>64_800</output>
64800   Answer= (64800)
<result>B</result>
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?