How-many-ways-can-this-be-done-if-you-distribute-25-identical-pieces-of-candy-among-five-children-

Question Number 134482 by benjo_mathlover last updated on 04/Mar/21

How many ways can this be done if you distribute 25 identical pieces of candy among five children?

Commented by mr W last updated on 04/Mar/21

{y o u}^{'} l l g e t p r o b l e m i f y o u {d o n}^{'} t g i v e

e a c h c h i l d 5 p i e c e s! :)

m a t h e m a t i c a l l y t o g e t a n u n i q u e

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

c h i l d m a y g e t n o t h i n g o r m u s t g e t

a t l e a s t o n e p i e c e . i f i w e r e y o u, i^{'} l l

a d d i f e a c h c h i l d m u s t g e t a t l e a s t

t w o p i e c e s .

Commented by benjo_mathlover last updated on 04/Mar/21

hello sir, that's the problem written in the book no other explanation

Commented by mr W last updated on 04/Mar/21

t h e n {i t}^{'} s a s s u m e d t h a t a b o x (h e r e a

c h i l d) m a y b e e m p t y . i n t h i s c a s e

t h e r e a r e C_{4}^{25 + 4} = \frac{29!}{25! 4!} = 23751 w a y s .

Commented by mr W last updated on 04/Mar/21

i f e a c h c h i l d m u s t g e t a t l e a s t

t w o p i e c e s, t h e n w e h a v e i n f a c t o n l y

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

C_{4}^{15 + 4} = 3876 w a y s .

Commented by benjo_mathlover last updated on 04/Mar/21

ok sir . thanks