How-many-words-can-you-form-using-the-letters-in-UNUSUALLY-such-that-no-same-letters-are-next-to-each-other-Answer-10200-

Question Number 107451 by mr W last updated on 11/Aug/20

H o w m a n y w o r d s c a n y o u f o r m u s i n g

t h e l e t t e r s i n U N U S U A L L Y

s u c h t h a t n o s a m e l e t t e r s a r e n e x t

t o e a c h o t h e r ?

[A n s w e r : 10200]

Commented by I want to learn more last updated on 11/Aug/20

Please i will love to see the workings sir . Please

Answered by mr W last updated on 11/Aug/20

U U U \Rightarrow

N S A Y L L \Rightarrow

t o a r r a n g e t h e r e a r e \frac{6!}{2!} w a y s

t o p l a c e 3 U i n t h e r e a r e C_{3}^{7} w a y s

\Rightarrow C_{3}^{7} \times \frac{6!}{2!} w o r d s

i n c l u s i v e w o r d s w i t h b o t h L t o g e t h e r!

U U U \Rightarrow

N S A Y (L L) \Rightarrow w i t h b o t h L t o g e t h e r

t o a r r a n g e t h e r e a r e 5! w a y s

t o p l a c e 3 U i n t h e r e a r e C_{3}^{6} w a y s

\Rightarrow C_{3}^{6} \times 5! w o r d s

r e q u e s t e d r e s u l t :

C_{3}^{7} \times \frac{6!}{2!} - C_{3}^{6} \times 5! = 10200 w o r d s

Commented by I want to learn more last updated on 11/Aug/20

Wow, thanks sir .