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

Question

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 (A) 19 ⋅ 5 ! (B) 4 ⋅ 5 ! (C) ((19/4)) ⋅ 5 ! (D) (3/4) ⋅ 5 !

Tardigrade Admin · Accepted Answer

HUDHUDBIRD ⇒ (DDD), (HH), (UU), B, I, R (i) 3 A +2 OA +1 D ⇒ 1 × 2 C 1 × 4 C 1 × (6 !/3 ! 2 !)=4 ⋅ 5 ! (ii) 2 A +2 OA +2 OOA = 3 C 3 × (6 !/2 ! 2 ! 2 !)=(3/4) ⋅ 5 ! ∴ Total number of words =(4+(3/4)) ⋅ 5 !=((19/4)) ⋅ 5 !

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

$19 \cdot 5!$

$4 \cdot 5$ !

$(\frac{19}{4}) \cdot 5$ !

$\frac{3}{4} \cdot 5!$

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

19⋅5!

4⋅5 !

(419​)⋅5 !

43​⋅5!

HUDHUDBIRD ⇒ (DDD), (HH), (UU), B, I, R (i) 3A+2OA+1D⇒1×2C1​×4C1​×3!2!6!​=4⋅5! (ii) 2A+2OA+2OOA=3C3​×2!2!2!6!​=43​⋅5! ∴ Total number of words =(4+43​)⋅5!=(419​)⋅5!

$19 \cdot 5!$

$4 \cdot 5$ !

$(\frac{19}{4}) \cdot 5$ !

$\frac{3}{4} \cdot 5!$