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


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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

	$Wow, thanks sir .$
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