How-many-permutation-can-be-made-using-the-word-CANADA-each-of-the-six-letter-being-used-mixed-in-each-permutation-In-how-many-of-these-permutation-will-the-three-A-s-be-together-In-how-many-will-

Question Number 40284 by scientist last updated on 18/Jul/18

H o w m a n y p e r m u t a t i o n c a n b e m a d e u s i n g t h e w o r d

C A N A D A e a c h o f t h e s i x l e t t e r b e i n g u s e d m i x e d

i n e a c h p e r m u t a t i o n ? I n h o w m a n y o f t h e s e

p e r m u t a t i o n w i l l t h e t h r e e A^{'} s b e t o g e t h e r ? I n

h o w m a n y w i l l t w o A^{'} s b e t o g e t h e r b u t n o t t h e t h r e e ?

Answered by tanmay.chaudhury50@gmail.com last updated on 19/Jul/18

i) C A N A D A A = 3 C = 1 D = 1 N = 1

p e r m u t a i o n n u m b e r s = \frac{6!}{3!} = \frac{6 \times 5 \times 4 \times 3!}{3!} = 120

i i) l e t 03 n u m b e r s o f A f a v i q u i c k e d w i t h e a c h

o t h e r s o (A A A) C D N

p e r m u t a t i o n = 4! = 24

i i i) (A A) A C D N

p d r m u t a t i o n = 3 C_{2} \times 5! = 3 \times 120 = 360

p l s c h e c k \dots

a f t e r e d i t i n g \dots

i i i) r e q u i r e d a n s w e r i s 360 - 24 = 336

b e c o s o u t o f t h e s e 360 p e r m u t a t i o n 24

p e r m u t a t i o n a r e i n c l u d e d w h e r e 03 A A A w i l l

b e t o g e t h e r \dots s o a n s i s 360 - 24 = 336

Commented by MJS last updated on 18/Jul/18

i i i) might be wrong because A A A is not

allowed but I^{'} m not sure in these things

Commented by tanmay.chaudhury50@gmail.com last updated on 19/Jul/18

y e s y o u a r e r i g h t \dots i a m e d i t i n g \dots