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Q.
The number of six lettered words which can be formed from the letters of the word 'HUDHUDBIRD' if each word contains not more than three distinct letters is
Permutations and Combinations
Solution:
HUDHUDBIRD $\Rightarrow$ (DDD), (HH), (UU), B, I, R
(i) $ 3 A +2 OA +1 D \Rightarrow 1 \times{ }^2 C _1 \times{ }^4 C _1 \times \frac{6 !}{3 ! 2 !}=4 \cdot 5 !$
(ii) $ 2 A +2 OA +2 OOA ={ }^3 C _3 \times \frac{6 !}{2 ! 2 ! 2 !}=\frac{3}{4} \cdot 5 !$
$\therefore$ Total number of words $=\left(4+\frac{3}{4}\right) \cdot 5 !=\left(\frac{19}{4}\right) \cdot 5 !$