1 A special kind of code word consists of 4 upper case lette

1- A special kind of code word consists of 4 upper case letters where exactly two of the letters must be the same and the others different. Thus in total we have 3 different letters appearing. How many such code words are there?

2- What if we require that 3 of the letters be the same and one is different. How many code words are there now?

Solution

IF the two same letters are A and A, the remaining 2 letters can be chosen in 25*24 = 600 ways

Now, the 2 A\'s can also be arranged in a total of 6 ways

So, 600*6 = 3600 ways

Like this, we can have BB , CC , DD , ..... ZZ

So, total possibilities ---> 3600 * 26

93600 possibilities --> first answer

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AAA ---> other letter can be any of the other 25 possibilities

AAA can be arranged in 4 ways

So, 25 * 4 = 100 when the repeated letter is A

Like this, we can have BBB , CCC , .... , ZZZ

So, 26 * 100

2600 possibilities