Question

The total number of $4$ letter words that can be formed from the string $"AABBBBCC"$ is

• A. $56$
• B. $68$
• C. $63$
• D. $48$

Answer 1

The correct option is C $63$

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) $={}^3{C}_2\times \frac{4!}{2!2!}=18$ ways.

$3.XXYZ$ (two same and remaining two are different)
$={}^3{C}_1\times \frac{4!}{2!}=36$ ways

$4.XXXY$ (three same and remaining one is different)
$={}^2{C}_1\times \frac{4!}{3!}=8$

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