To choose a password for our newest computer system, 26 tiles (each containing a

Question

To choose a password for our newest computer system, 26 tiles (each containing a different letter of the alphabet) are placed into a bag. At each stage of the selction process, two tiles are chosen from the bag. From these two tiles one tile is chosen at random and becomes the first letter in the password. Both tiles are then discarded (so neither can be chosen again). This procedure continues until a 6 character password has been formed.

1. How many passwords may be created following this algorithm?

2. Which of the following can be formed using this algorithm: AMOEBA, OXYGEN, IMPORT? (explain why the password is impossible or show a sequence of tile choices that results in the password)

Explanation / Answer

For 6 character password:

the first letter is choosen in 26C2* 1/2 ways

second letter in 24C2* 1/2 ways

third letter in 22C2* 1/2 ways

fourth letter in 20C2* 1/2 ways

fifth letter in 18C2* 1/2 ways

sixth letter in 16C2* 1/2 ways

total ways =(1/2)6 (26C2*24C2*22C2*20C2*18C2*16C2)

=1129 * 109 ways

b) the letter AMOEBA cant be formed in this method

since it contains 2 letters A which is not possible.

because whwn first letter A is choosen, it is discarded and cant be selected again for sixth letter

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