8 digit numbers are formed using 1 1 2 2 2 3 4 4. The number of such numbers in which the odd digits do not occupy odd places is a)160 b)120 c)60 d)48


Question and Answers Forum

All Questions Topic List
Permutation and Combination Questions
Previous in All Question Next in All Question
Previous in Permutation and Combination Next in Permutation and Combination
Question Number 52278 by Necxx last updated on 05/Jan/19

$8 d i g i t n u m b e r s a r e f o r m e d u s i n g$ $1 1 2 2 2 3 4 4 . T h e n u m b e r o f s u c h$ $n u m b e r s i n w h i c h t h e o d d d i g i t s$ $d o n o t o c c u p y o d d p l a c e s i s$ $a) 1 60 b) 120 c) 60 d) 48$
	Answered by tanmay.chaudhury50@gmail.com last updated on 06/Jan/19

	$\underset{8}{-} \underset{7}{-} \underset{6}{-} \underset{5}{-} \underset{4}{-} \underset{3}{-} \underset{2}{-} \underset{1}{-}$ $o d d p l a c e a r e (1, 3, 5, 7)$ $e v e n p l a c e (2, 4, 6, 8)$ $o d d d i g i t (1, 1, 3) \to t h r e e$ $e v e n d i g i t (2, 2, 2, 4, 4) \to f i v e$ $n o w$ $p l a c e 1, 3, 5, 7 t o b e f i l l e d b y e v e n d i g i t s (2, 2, 2, 4, 4)$ $s o n u m b e r s o f w a y i s = \frac{5 \times 4 \times 3 \times 2}{3! \times 2!} = 10$ $[d e n o m i n a t o r 3! f o r (2, 2, 2) a n d 2! f o r (4, 4)]$ $r e m a n i n g f o u r p l a c e (2, 4, 6, 8)$ $r r m a i n i n g d i g i t (1, 1, 3) n d o n e e v e n d i g i t$ $w a y s = \frac{4 \times 3 \times 2 \times 1}{2!} = 12$ $o u t o f t h e s e (10 \times 12) = 120$
	Commented by mr W last updated on 06/Jan/19

	$w h a t i s y o u r f i n a l r e s u l t s i r ?$
	Commented by tanmay.chaudhury50@gmail.com last updated on 06/Jan/19

	$t h a n k y o u s i r . . . c l u e i s i n y o u r a n s w e r . . .$
	Commented by mr W last updated on 06/Jan/19

	$t h a n k s f o r c o n f i r m i n g s i r!$
	Commented by Necxx last updated on 06/Jan/19

	$I j u s t l o v e t h i s e x p l a n a t i o n . T h a n k$ $y o u s i r T a n m a y .$
	Answered by mr W last updated on 06/Jan/19

	$t h e o n l y r e s t r i c t i o n : o d d d i g i t s {d o n}^{'} t o c c u p y$ $o d d p l a c e s, i . e . t h e t h r e e d i g i t s 1, 1, 3$ $c a n o n l y b e p l a c e d i n 4 e v e n p o s i t i o n s .$ $t o a r r a n g e t h e t h r e e o d d d i g i t s (1, 1, 3)$ $i n 4 e v e n p o s i t i o n s t h e r e a r e$ $\frac{P_{3}^{4}}{2!} d i f f e r e n t w a y s .$ $t o a r r a n g e t h e r e m a i n i n g 5 e v e n$ $d i g i t s (2, 2, 2, 4, 4) i n t h e r e m a i n i n g 5$ $p o s s i t i o n s t h e r e a r e$ $\frac{5!}{2! 3!} d i f f e r e n t w a y s .$ $s o t h e r e s u l t i s \frac{P_{3}^{4}}{2!} \times \frac{5!}{2! 3!} = \frac{4 \times 3 \times 2}{2} \times \frac{5 \times 4}{2} = 120$ $\Rightarrow a n s w e r b) i s c o r r e c t$
	Commented by Necxx last updated on 06/Jan/19

	$y e a h . . . . v e r y e x p l a n a t o r y . T h a n k s$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum