ruis wrote:
In a law firm, each case is to be designated by a three-letter-code in which no letter can be used more than twice. If there are 26 letters to choose from, how many different codes are available? Two codes with the same letters in a different order are considered different codes.
A. 26^3
B. 27*26*25
C. 26^2 *25
D. 26*25*3
E.26*25*24
Different arrangements gives us different codes. Each letter can be used multiple times (for now, let's ignore the no more than twice restriction).
In this case, we will use the fundamental counting principle.
So the number of codes will simply be = 26 * 26 * 26
The only limitation is that a letter cannot be used thrice i.e. AAA, GGG etc are not acceptable. How many such cases are there? Only 26 because there are 26 letters.
Hence acceptable codes\( = 26^3 - 26 = 26 (26^2 - 1) = 26 * (26+1)(26 -1) =27*26*25\)
Answer (B)
Check fundamental counting principle here in thisvideo.
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Statistics : Posted by KarishmaB • on 02 Mar 2024, 04:09 • Replies 2 • Views 99
