In-how-many-ways-can-30-students-be-distributed-to-10-schools-if-1-each-school-should-get-at-least-one-student-2-no-restriction-

Question Number 158529 by mr W last updated on 11/Nov/21

I n h o w m a n y w a y s c a n 30 s t u d e n t s

b e d i s t r i b u t e d t o 10 s c h o o l s, i f

1 . e a c h s c h o o l s h o u l d g e t a t l e a s t o n e

s t u d e n t .

2 . n o r e s t r i c t i o n

Answered by cortano last updated on 06/Nov/21

\Rightarrow x_{1} + x_{2} + \dots + x_{10} = 30; x_{i} ⩾ 1

\Rightarrow (\begin{matrix} 30 - 1 \\ 10 - 1 \end{matrix}) = (\begin{matrix} 29 \\ 9 \end{matrix}) = \frac{29!}{9! 20!}

Commented by mr W last updated on 07/Nov/21

t h i s i s o n l y t r u e, w h e n 30 (i d e n t i c a l)

c o m p u t e r s a r e d i s t r i b u t e d t o 10

s c h o o l s . b u t h e r e t h e 30 s t u d e n t s

a r e d i f f e r e n t o b j e c t s, s o t h e a n s w e r

i s n o t c o r r e c t .

Commented by ajfour last updated on 06/Nov/21

i h a d g o t

(1) 10!^{30} C_{10} \times 10^{20}

(2) 10^{30}

Commented by mr W last updated on 06/Nov/21

t h e r e s u l t f o r (1) s e e m s t o b e l o g i c,

b u t i t i s i n f a c t n o t c o r r e c t, b e c a u s e

i t i s l a r g e r t h a n t h e a n s w e r t o (2),

a n d t h i s c a n n o t b e t r u e, s i n c e

t h e w a y s w i t h r e s t r i c t i o n m u s t b e

l e s s t h a n t h e w a y s w i t h o u t r e s t r i c t i o n .

s o w h e r e i s t h e e r r o r ?

Commented by mr W last updated on 11/Nov/21

c o r r e c t s o l u t i o n s e e Q 158955

Facebook Tweet Pin