Question

How many ways are there to pass out 20 candies (all candies are identical) to 6 children? Based on the following conditions:

-No restriction

-Every child receives at least one candy.

-No child receives the same number of candies.

Answer 1

first consider that every child receives the same number of candies

if n_c denotes the number of candies received by each children. then 6*n_c is less than or equal to 20, which implies n_c is less than or equal to 3.4.

so each children can get either 1 cady or 2 candies or 3 candies if each of them get the same number candies.

so number of ways that each child gets the same number of candies= 3

[

considering the fact that 20 candies are distributed rather than distributing no candy at all.

if no candy is distributed then each child will get zero candy considering the fact that  each of them get the same number candies.

we are ommiting that possible way.

]

number of ways no child receives the same number of candies = total number of ways 20 candies can be given to 6 children-number of ways each of 6 children get the same number of candies

=11628-3 ways= 11625 ways

Dear student I have tried my best of knowledge to give you clear idea.

if you like my answer. please rate my answer .Thank you !!!!