A-square-is-divided-into-9-identical-smaller-squares-Six-identical-balls-are-to-be-placed-in-these-smaller-squares-such-that-each-of-the-three-rows-gets-at-least-one-ball-one-ball-in-one-square-only-

Question Number 47656 by Necxx last updated on 12/Nov/18

A s q u a r e i s d i v i d e d i n t o 9 i d e n t i c a l

s m a l l e r s q u a r e s . S i x i d e n t i c a l b a l l s

a r e t o b e p l a c e d i n t h e s e s m a l l e r

s q u a r e s s u c h t h a t e a c h o f t h e t h r e e

r o w s g e t s a t l e a s t o n e b a l l (o n e

b a l l i n o n e s q u a r e o n l y) . I n h o w

m a n y d i f f e r e n t w a y s c a n t h i s b e

d o n e ?

a) 9 1 b) 51 c) 81 d) 41

Commented by Necxx last updated on 13/Nov/18

p l e a s e h e l p

Answered by tanmay.chaudhury50@gmail.com last updated on 13/Nov/18

c o m b i n a t i o n \dots l e t d e n o t e

f i r s t r o w = F R s i m i l a r l y S R, T R

1) F R = 1 S R = 2 T R = 3 \to 9 w a y s

2) F R = 2 S R = 3 T R = 1 \to 9 w a y s

3) F R = 3 S R = 2 T R = 1 \to 9 w a y s

4) F R = 2 S R = 2 T R = 2 \to 27 w a y s

5) F R = 3 S R = 1 T R = 2 \to 9 w a y s

6) F R = 2 S R = 1 T R = 3 \to 9 w a y s

7) F R = 1 S R = 3 T R = 2 \to 9 w a y s

(1) 3 c_{1} \times 3 c_{2} \times 3 c_{3} = 9 \leftarrow e x a m p l e o f c a l c u l a t i o n f o r

f i r s t c a s e t h a t i s F R = 1 S R = 2 T R = 3

o t h e r s s i m i l a r w a y c a l c u l a t e d)

s o t o t a l 9 \times 6 + 27 = 81

Commented by Necxx last updated on 13/Nov/18

w o w \dots . . T h a n k y o u s o m u c h .

Facebook Tweet Pin