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Question

The total number of 4 letter words that can be formed from the string "AABBBBCC" is
  1. 56
  2. 48
  3. 68
  4. 63


Solution

The correct option is D 63
Available letters :A,B,C
Here following patterns are possible:
 
1.  XXXX   (all four letters are same) only BBBB, so only 1 way.

2.  XXYY   (two same and remaining two are also same) = 3C2×4!2!2!=18 ways.

3.  XXYZ (two same and remaining two are different)
= 3C1×4!2!=36 ways

4.  XXXY (three same and remaining one is different)
= 2C1×4!3!=8

Now, required number of ways :
=1+18+36+8=63
 

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