There are 6 distinct letters of the English alphabet and 4 d

Total number of digits in the code is 6.
Out of this 6, 4 are alphabets = 6C4 ways=15
The other 2 are numeric digits = 4C2 ways=6

Now these 6 digits can be arranged among themselves in 6! ways.
So, the answer is 15*6*6!=64800

is this a 700 level Q? I doubt..

Let’s first find the number of codes in the format LLLLDD where L denotes a letter and D denotes a digit. We must choose exactly 4 of 6 letters, and repeats are not allowed for any individual code. Since order matters, there are 6P4 ways to choose the letters. Similarly, from 4 digits, we must choose 2, and repeats in any individual code are not allowed. Since order matters, this can be done in 4P2 ways.

Thus, the number of possible digit/code combinations of the format LLLLDD is:

6P4 x 4P2 = (6 x 5 x 4 x 3) x (4 x 3) = 360 x 12 = 4,320

Next, let’s find the number of different formats (such as LLDLLD or DDLLLL etc.) that one can create a code. We notice that LLLLDD can be arranged in 6!/(4!*2!) = (6 x 5)/2 = 15 ways. Any one of these 15 formats has the same number of codes as LLLLDD; therefore there are a total of 4,320 x 15 = 64,800 possible codes.

Answer: B

Given: 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.

Asked: If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?

Maximum number of codes that can be generated = 6C4 * 4C2 * 6! = 15*6*720 = 64800

IMO B

Hello Scott,

I understand the first part of determining 4,320 different combinations within the LLLLDD format. However, the question/prompt indicates that each letter and digit are distinct or different, so from a fundamental standpoint point why don't we multiply 4320 by 6! ?

Hence it may be X Y Z W 3 4 = 6 x 5 x 4 x 3 x 2 x 1 ways to arrange those 6 different entities/items.